Calculating Derivative – A function with e – Exercise 1017

Exercise

Find the derivative of the following function:

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

Final Answer

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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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