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Calculating Derivative – A function with e – Exercise 1017

Exercise

Find the derivative of the following function:

f(x)={(1+e^{-x})}^7

Final Answer


f'(x)=-7e^{-x}{(1+e^{-x})}^6

Solution

Using Derivative formulas and chain rule in Derivative Rules, we get the derivative:

f'(x)=7{(1+e^{-x})}^6\cdot (1+e^{-x})'=

=7{(1+e^{-x})}^6\cdot (-e^{-x})=

=-7e^{-x}{(1+e^{-x})}^6

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