What is the derivative of (1-e^x)/(1+e^x) ?

The derivative of (1-e^x)/(1+e^x) is -(2e^x)/((1+e^x)^2)

What is the first derivative of (1-e^x)/(1+e^x) ?

The first derivative of (1-e^x)/(1+e^x) is -(2e^x)/((1+e^x)^2)

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derivative of

\frac{1 - e ^{x}}{1 + e ^{x}}

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

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Simplify

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

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

2 ln (x^{2} + 1)

2 + x

\frac{1}{( 1 + x )}

\frac{x ^{3}}{2} + \frac{1}{x ^{2}}

x^{6} + x^{3} + 2

What is the derivative of (1-e^x)/(1+e^x) ?
The derivative of (1-e^x)/(1+e^x) is -(2e^x)/((1+e^x)^2)
What is the first derivative of (1-e^x)/(1+e^x) ?
The first derivative of (1-e^x)/(1+e^x) is -(2e^x)/((1+e^x)^2)