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How do you find the derivative of #f(x) = e^x + e^(-x / 2)#?

Answer 1

Ezra Adams

#f'(x)=e^x-1/(2e^x)#

Rule : #d/dx e^(u(x))=e^u*(du)/dx#.

Application thereof :

#d/dx[e^x+e^(-x/2)]=e^x-1/2e^(-x)#

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Answer 2

Ezra Adams

To find the derivative of ( f(x) = e^x + e^{-x/2} ), apply the differentiation rules. The derivative of ( e^x ) is ( e^x ), and the derivative of ( e^{-x/2} ) is ( -\frac{1}{2} e^{-x/2} ). Therefore, the derivative of ( f(x) ) is ( f'(x) = e^x - \frac{1}{2} e^{-x/2} ).

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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.

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