# How do you find the derivative of #y=sin2x+cos2x+ln(ex)#?

Your expression is

Differentiating throughout with respect to x,

You can now apply the chain rule of differentiation to the first two terms on the right hand side of the equation, to get this

The last term is a constant, so its derivative is 0.

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To find the derivative of ( y = \sin(2x) + \cos(2x) + \ln(e^x) ), use the chain rule and the derivative rules for trigonometric and logarithmic functions. The derivativeTo find the derivative of ( y = \sin(2x) + \cos(2x) + \ln(e^x) ), you can apply the chain rule and the derivatives of trigonometric functions and logarithmic functions.

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( \frac{dTo find the derivative of ( y = \sin(2x) + \cos(2x) + \ln(e^x) ), use the chain rule and the derivative rules for trigonometric and logarithmic functions. The derivative is:

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( \frac{d}{To find the derivative of ( y = \sin(2x) + \cos(2x) + \ln(e^x) ), use the chain rule and the derivative rules for trigonometric and logarithmic functions. The derivative is:

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( \frac{d}{dx}(\sin(2xTo find the derivative of ( y = \sin(2x) + \cos(2x) + \ln(e^x) ), use the chain rule and the derivative rules for trigonometric and logarithmic functions. The derivative is:

[ \frac{dy}{dx} = 2To find the derivative of ( y = \sin(2x) + \cos(2x) + \ln(e^x) ), you can apply the chain rule and the derivatives of trigonometric functions and logarithmic functions.

( \frac{d}{dx}(\sin(2x))To find the derivative of ( y = \sin(2x) + \cos(2x) + \ln(e^x) ), use the chain rule and the derivative rules for trigonometric and logarithmic functions. The derivative is:

[ \frac{dy}{dx} = 2\To find the derivative of ( y = \sin(2x) + \cos(2x) + \ln(e^x) ), you can apply the chain rule and the derivatives of trigonometric functions and logarithmic functions.

( \frac{d}{dx}(\sin(2x)) =To find the derivative of ( y = \sin(2x) + \cos(2x) + \ln(e^x) ), use the chain rule and the derivative rules for trigonometric and logarithmic functions. The derivative is:

[ \frac{dy}{dx} = 2\cosTo find the derivative of ( y = \sin(2x) + \cos(2x) + \ln(e^x) ), you can apply the chain rule and the derivatives of trigonometric functions and logarithmic functions.

( \frac{d}{dx}(\sin(2x)) = To find the derivative of ( y = \sin(2x) + \cos(2x) + \ln(e^x) ), use the chain rule and the derivative rules for trigonometric and logarithmic functions. The derivative is:

[ \frac{dy}{dx} = 2\cos(To find the derivative of ( y = \sin(2x) + \cos(2x) + \ln(e^x) ), you can apply the chain rule and the derivatives of trigonometric functions and logarithmic functions.

( \frac{d}{dx}(\sin(2x)) = 2To find the derivative of ( y = \sin(2x) + \cos(2x) + \ln(e^x) ), use the chain rule and the derivative rules for trigonometric and logarithmic functions. The derivative is:

[ \frac{dy}{dx} = 2\cos(2To find the derivative of ( y = \sin(2x) + \cos(2x) + \ln(e^x) ), you can apply the chain rule and the derivatives of trigonometric functions and logarithmic functions.

( \frac{d}{dx}(\sin(2x)) = 2\To find the derivative of ( y = \sin(2x) + \cos(2x) + \ln(e^x) ), use the chain rule and the derivative rules for trigonometric and logarithmic functions. The derivative is:

[ \frac{dy}{dx} = 2\cos(2xTo find the derivative of ( y = \sin(2x) + \cos(2x) + \ln(e^x) ), you can apply the chain rule and the derivatives of trigonometric functions and logarithmic functions.

( \frac{d}{dx}(\sin(2x)) = 2\cosTo find the derivative of ( y = \sin(2x) + \cos(2x) + \ln(e^x) ), use the chain rule and the derivative rules for trigonometric and logarithmic functions. The derivative is:

[ \frac{dy}{dx} = 2\cos(2x)To find the derivative of ( y = \sin(2x) + \cos(2x) + \ln(e^x) ), you can apply the chain rule and the derivatives of trigonometric functions and logarithmic functions.

( \frac{d}{dx}(\sin(2x)) = 2\cos(To find the derivative of ( y = \sin(2x) + \cos(2x) + \ln(e^x) ), use the chain rule and the derivative rules for trigonometric and logarithmic functions. The derivative is:

[ \frac{dy}{dx} = 2\cos(2x) -To find the derivative of ( y = \sin(2x) + \cos(2x) + \ln(e^x) ), you can apply the chain rule and the derivatives of trigonometric functions and logarithmic functions.

( \frac{d}{dx}(\sin(2x)) = 2\cos(2To find the derivative of ( y = \sin(2x) + \cos(2x) + \ln(e^x) ), use the chain rule and the derivative rules for trigonometric and logarithmic functions. The derivative is:

[ \frac{dy}{dx} = 2\cos(2x) - To find the derivative of ( y = \sin(2x) + \cos(2x) + \ln(e^x) ), you can apply the chain rule and the derivatives of trigonometric functions and logarithmic functions.

( \frac{d}{dx}(\sin(2x)) = 2\cos(2xTo find the derivative of ( y = \sin(2x) + \cos(2x) + \ln(e^x) ), use the chain rule and the derivative rules for trigonometric and logarithmic functions. The derivative is:

[ \frac{dy}{dx} = 2\cos(2x) - 2To find the derivative of ( y = \sin(2x) + \cos(2x) + \ln(e^x) ), you can apply the chain rule and the derivatives of trigonometric functions and logarithmic functions.

( \frac{d}{dx}(\sin(2x)) = 2\cos(2x)To find the derivative of ( y = \sin(2x) + \cos(2x) + \ln(e^x) ), use the chain rule and the derivative rules for trigonometric and logarithmic functions. The derivative is:

[ \frac{dy}{dx} = 2\cos(2x) - 2\To find the derivative of ( y = \sin(2x) + \cos(2x) + \ln(e^x) ), you can apply the chain rule and the derivatives of trigonometric functions and logarithmic functions.

( \frac{d}{dx}(\sin(2x)) = 2\cos(2x) \To find the derivative of ( y = \sin(2x) + \cos(2x) + \ln(e^x) ), use the chain rule and the derivative rules for trigonometric and logarithmic functions. The derivative is:

[ \frac{dy}{dx} = 2\cos(2x) - 2\sinTo find the derivative of ( y = \sin(2x) + \cos(2x) + \ln(e^x) ), you can apply the chain rule and the derivatives of trigonometric functions and logarithmic functions.

( \frac{d}{dx}(\sin(2x)) = 2\cos(2x) )

To find the derivative of ( y = \sin(2x) + \cos(2x) + \ln(e^x) ), use the chain rule and the derivative rules for trigonometric and logarithmic functions. The derivative is:

[ \frac{dy}{dx} = 2\cos(2x) - 2\sin(To find the derivative of ( y = \sin(2x) + \cos(2x) + \ln(e^x) ), you can apply the chain rule and the derivatives of trigonometric functions and logarithmic functions.

( \frac{d}{dx}(\sin(2x)) = 2\cos(2x) )

(To find the derivative of ( y = \sin(2x) + \cos(2x) + \ln(e^x) ), use the chain rule and the derivative rules for trigonometric and logarithmic functions. The derivative is:

[ \frac{dy}{dx} = 2\cos(2x) - 2\sin(2To find the derivative of ( y = \sin(2x) + \cos(2x) + \ln(e^x) ), you can apply the chain rule and the derivatives of trigonometric functions and logarithmic functions.

( \frac{d}{dx}(\sin(2x)) = 2\cos(2x) )

( \To find the derivative of ( y = \sin(2x) + \cos(2x) + \ln(e^x) ), use the chain rule and the derivative rules for trigonometric and logarithmic functions. The derivative is:

[ \frac{dy}{dx} = 2\cos(2x) - 2\sin(2xTo find the derivative of ( y = \sin(2x) + \cos(2x) + \ln(e^x) ), you can apply the chain rule and the derivatives of trigonometric functions and logarithmic functions.

( \frac{d}{dx}(\sin(2x)) = 2\cos(2x) )

( \fracTo find the derivative of ( y = \sin(2x) + \cos(2x) + \ln(e^x) ), use the chain rule and the derivative rules for trigonometric and logarithmic functions. The derivative is:

[ \frac{dy}{dx} = 2\cos(2x) - 2\sin(2x)To find the derivative of ( y = \sin(2x) + \cos(2x) + \ln(e^x) ), you can apply the chain rule and the derivatives of trigonometric functions and logarithmic functions.

( \frac{d}{dx}(\sin(2x)) = 2\cos(2x) )

( \frac{To find the derivative of ( y = \sin(2x) + \cos(2x) + \ln(e^x) ), use the chain rule and the derivative rules for trigonometric and logarithmic functions. The derivative is:

[ \frac{dy}{dx} = 2\cos(2x) - 2\sin(2x) +To find the derivative of ( y = \sin(2x) + \cos(2x) + \ln(e^x) ), you can apply the chain rule and the derivatives of trigonometric functions and logarithmic functions.

( \frac{d}{dx}(\sin(2x)) = 2\cos(2x) )

( \frac{dTo find the derivative of ( y = \sin(2x) + \cos(2x) + \ln(e^x) ), use the chain rule and the derivative rules for trigonometric and logarithmic functions. The derivative is:

[ \frac{dy}{dx} = 2\cos(2x) - 2\sin(2x) + \To find the derivative of ( y = \sin(2x) + \cos(2x) + \ln(e^x) ), you can apply the chain rule and the derivatives of trigonometric functions and logarithmic functions.

( \frac{d}{dx}(\sin(2x)) = 2\cos(2x) )

( \frac{d}{To find the derivative of ( y = \sin(2x) + \cos(2x) + \ln(e^x) ), use the chain rule and the derivative rules for trigonometric and logarithmic functions. The derivative is:

[ \frac{dy}{dx} = 2\cos(2x) - 2\sin(2x) + \fracTo find the derivative of ( y = \sin(2x) + \cos(2x) + \ln(e^x) ), you can apply the chain rule and the derivatives of trigonometric functions and logarithmic functions.

( \frac{d}{dx}(\sin(2x)) = 2\cos(2x) )

( \frac{d}{dxTo find the derivative of ( y = \sin(2x) + \cos(2x) + \ln(e^x) ), use the chain rule and the derivative rules for trigonometric and logarithmic functions. The derivative is:

[ \frac{dy}{dx} = 2\cos(2x) - 2\sin(2x) + \frac{To find the derivative of ( y = \sin(2x) + \cos(2x) + \ln(e^x) ), you can apply the chain rule and the derivatives of trigonometric functions and logarithmic functions.

( \frac{d}{dx}(\sin(2x)) = 2\cos(2x) )

( \frac{d}{dx}To find the derivative of ( y = \sin(2x) + \cos(2x) + \ln(e^x) ), use the chain rule and the derivative rules for trigonometric and logarithmic functions. The derivative is:

[ \frac{dy}{dx} = 2\cos(2x) - 2\sin(2x) + \frac{1To find the derivative of ( y = \sin(2x) + \cos(2x) + \ln(e^x) ), you can apply the chain rule and the derivatives of trigonometric functions and logarithmic functions.

( \frac{d}{dx}(\sin(2x)) = 2\cos(2x) )

( \frac{d}{dx}(\To find the derivative of ( y = \sin(2x) + \cos(2x) + \ln(e^x) ), use the chain rule and the derivative rules for trigonometric and logarithmic functions. The derivative is:

[ \frac{dy}{dx} = 2\cos(2x) - 2\sin(2x) + \frac{1}{To find the derivative of ( y = \sin(2x) + \cos(2x) + \ln(e^x) ), you can apply the chain rule and the derivatives of trigonometric functions and logarithmic functions.

( \frac{d}{dx}(\sin(2x)) = 2\cos(2x) )

( \frac{d}{dx}(\cosTo find the derivative of ( y = \sin(2x) + \cos(2x) + \ln(e^x) ), use the chain rule and the derivative rules for trigonometric and logarithmic functions. The derivative is:

[ \frac{dy}{dx} = 2\cos(2x) - 2\sin(2x) + \frac{1}{eTo find the derivative of ( y = \sin(2x) + \cos(2x) + \ln(e^x) ), you can apply the chain rule and the derivatives of trigonometric functions and logarithmic functions.

( \frac{d}{dx}(\sin(2x)) = 2\cos(2x) )

( \frac{d}{dx}(\cos(To find the derivative of ( y = \sin(2x) + \cos(2x) + \ln(e^x) ), use the chain rule and the derivative rules for trigonometric and logarithmic functions. The derivative is:

[ \frac{dy}{dx} = 2\cos(2x) - 2\sin(2x) + \frac{1}{e^To find the derivative of ( y = \sin(2x) + \cos(2x) + \ln(e^x) ), you can apply the chain rule and the derivatives of trigonometric functions and logarithmic functions.

( \frac{d}{dx}(\sin(2x)) = 2\cos(2x) )

( \frac{d}{dx}(\cos(2To find the derivative of ( y = \sin(2x) + \cos(2x) + \ln(e^x) ), use the chain rule and the derivative rules for trigonometric and logarithmic functions. The derivative is:

[ \frac{dy}{dx} = 2\cos(2x) - 2\sin(2x) + \frac{1}{e^xTo find the derivative of ( y = \sin(2x) + \cos(2x) + \ln(e^x) ), you can apply the chain rule and the derivatives of trigonometric functions and logarithmic functions.

( \frac{d}{dx}(\sin(2x)) = 2\cos(2x) )

( \frac{d}{dx}(\cos(2xTo find the derivative of ( y = \sin(2x) + \cos(2x) + \ln(e^x) ), use the chain rule and the derivative rules for trigonometric and logarithmic functions. The derivative is:

[ \frac{dy}{dx} = 2\cos(2x) - 2\sin(2x) + \frac{1}{e^x}To find the derivative of ( y = \sin(2x) + \cos(2x) + \ln(e^x) ), you can apply the chain rule and the derivatives of trigonometric functions and logarithmic functions.

( \frac{d}{dx}(\sin(2x)) = 2\cos(2x) )

( \frac{d}{dx}(\cos(2x))To find the derivative of ( y = \sin(2x) + \cos(2x) + \ln(e^x) ), use the chain rule and the derivative rules for trigonometric and logarithmic functions. The derivative is:

[ \frac{dy}{dx} = 2\cos(2x) - 2\sin(2x) + \frac{1}{e^x} \To find the derivative of ( y = \sin(2x) + \cos(2x) + \ln(e^x) ), you can apply the chain rule and the derivatives of trigonometric functions and logarithmic functions.

( \frac{d}{dx}(\sin(2x)) = 2\cos(2x) )

( \frac{d}{dx}(\cos(2x)) =To find the derivative of ( y = \sin(2x) + \cos(2x) + \ln(e^x) ), use the chain rule and the derivative rules for trigonometric and logarithmic functions. The derivative is:

[ \frac{dy}{dx} = 2\cos(2x) - 2\sin(2x) + \frac{1}{e^x} ]To find the derivative of ( y = \sin(2x) + \cos(2x) + \ln(e^x) ), you can apply the chain rule and the derivatives of trigonometric functions and logarithmic functions.

( \frac{d}{dx}(\sin(2x)) = 2\cos(2x) )

( \frac{d}{dx}(\cos(2x)) = -To find the derivative of ( y = \sin(2x) + \cos(2x) + \ln(e^x) ), use the chain rule and the derivative rules for trigonometric and logarithmic functions. The derivative is:

[ \frac{dy}{dx} = 2\cos(2x) - 2\sin(2x) + \frac{1}{e^x} ]To find the derivative of ( y = \sin(2x) + \cos(2x) + \ln(e^x) ), you can apply the chain rule and the derivatives of trigonometric functions and logarithmic functions.

( \frac{d}{dx}(\sin(2x)) = 2\cos(2x) )

( \frac{d}{dx}(\cos(2x)) = -2To find the derivative of ( y = \sin(2x) + \cos(2x) + \ln(e^x) ), use the chain rule and the derivative rules for trigonometric and logarithmic functions. The derivative is:

[ \frac{dy}{dx} = 2\cos(2x) - 2\sin(2x) + \frac{1}{e^x} ]To find the derivative of ( y = \sin(2x) + \cos(2x) + \ln(e^x) ), you can apply the chain rule and the derivatives of trigonometric functions and logarithmic functions.

( \frac{d}{dx}(\sin(2x)) = 2\cos(2x) )

( \frac{d}{dx}(\cos(2x)) = -2\To find the derivative of ( y = \sin(2x) + \cos(2x) + \ln(e^x) ), use the chain rule and the derivative rules for trigonometric and logarithmic functions. The derivative is:

( \frac{d}{dx}(\sin(2x)) = 2\cos(2x) )

( \frac{d}{dx}(\cos(2x)) = -2\sin(2x) )

( \frac{d}{dx}(\ln(e^x)) = \frac{1}{e^x} )

Putting it all together, the derivative of ( y ) with respect to ( x ) is:

( \frac{d}{dx}(y) = 2\cos(2x) - 2\sin(2x) + \frac{1}{e^x} )

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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