# How do you find the derivative of #y=1+x-cosx#?

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To find the derivative of ( y = 1 + x - \cos(x) ), use the sum rule and the derivative of cosine function:

( \frac{d}{dx}(1) = 0 )

( \frac{d}{dx}(x) = 1 )

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

So, the derivative of ( y ) with respect to ( x ) is:

( \frac{dy}{dx} = 1 - \sin(x) )

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To find the derivative of ( y = 1 + x - \cos(x) ), apply the derivative rules:

[ \frac{dy}{dx} = \frac{d}{dx} (1) + \frac{d}{dx} (x) - \frac{d}{dx} (\cos(x)) ]

[ \frac{dy}{dx} = 0 + 1 - (-\sin(x)) ]

[ \frac{dy}{dx} = 1 + \sin(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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