Exercise
Find the derivative of the following function:
f(x)=\frac{e^x-1}{e^x+1}
Final Answer
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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