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How do you find the derivative of #e ^(sin (2x))#?

Answer 1

Scarlett Allison

I would use the Chain Rule: #y'=e^(sin(2x))*2cos(2x)#

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Answer 2

Isaiah Allen

To find the derivative of ( e^{\sin(2x)} ), you can use the chain rule. First, differentiate the outer function with respect to its inner function, and then multiply by the derivative of the inner function.

( \frac{d}{dx}[e^{\sin(2x)}] = e^{\sin(2x)} \cdot \frac{d}{dx}[\sin(2x)] )

Now, differentiate the inner function, which is ( \sin(2x) ). The derivative of ( \sin(2x) ) with respect to ( x ) is ( 2\cos(2x) ).

So, the derivative of ( e^{\sin(2x)} ) with respect to ( x ) is ( e^{\sin(2x)} \cdot 2\cos(2x) ).

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Answer from HIX Tutor

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.