# If #f(x)=sin x# and #g(x)=e^x#, why is #f'(x)=cos x# and #g'(x)=e^x#?

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The derivative of ( f(x) = \sin(x) ) is ( f'(x) = \cos(x) ) because the derivative of the sine function is the cosine function.

The derivative of ( g(x) = e^x ) is ( g'(x) = e^x ) because the exponential function ( e^x ) is its own derivative.

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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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