Home > Calculus > Differentiating Exponential Functions with Base e

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

Answer 1

Aurora Alvarado

#e^xcos(e^x)#

differentiate using the #color(blue)"chain rule"#

#"Given" f(x)=g(h(x))" then"#

#• f'(x)=g'(h(x))xxh'(x)#

#rArrf(x)=sin(e^x)#

#rArrf'(x)=cos(e^x)xxd/dx(e^x)#

#color(white)(rArrf'(x))=e^xcos(e^x)#

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Answer 2

Isabella Ackerman

To find the derivative of ( \sin(e^x) ), we apply the chain rule. The derivative of ( \sin(u) ) is ( \cos(u) ), and the derivative of ( e^x ) with respect to ( x ) is ( e^x ). Therefore, the derivative of ( \sin(e^x) ) is ( \cos(e^x) \cdot e^x ).

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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.