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Calculating Derivative – A quotient of exponential functions – Exercise 6335

Exercise

Find the derivative of the following function:

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

Final Answer


f'(x)=\frac{2e^x}{{(e^x+1)}^2}

Solution

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

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

f'(x)=\frac{e^x(e^x+1)-(e^x-1)\cdot e^x}{{(e^x+1)}^2}=

One can simplify the derivative:

=\frac{e^{2x}+e^x-e^{2x}+ e^x}{{(e^x+1)}^2}=

=\frac{2e^x}{{(e^x+1)}^2}

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