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

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

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

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

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Popular >

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Expand

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

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

\frac{\partial}{\partial x} (ln (5 x + 2 y))

x \to 6 lim (1)

ln (1 + x), at (x = 2)

3 x^{2} - 4 x

e^{x - 1}, 0

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