What is (\partial)/(\partial x)((ln(1+e^{(x)}))^2) ?

The answer to (\partial)/(\partial x)((ln(1+e^{(x)}))^2) is (2e^xln(1+e^x))/(1+e^x)

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(\partial)/(\partial x)((ln(1+e^{(x)}))^2)

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

t \to 0 lim (\frac{2 e ^{t} - 2}{t})

\int 2 + 2 cos (x) d x

\int \frac{1}{3 - 4 x - x ^{2}} d x

d y = (x - 2 y cot (2 x)) d x

x (8 x + 5)^{4}

What is (\partial)/(\partial x)((ln(1+e^{(x)}))^2) ?
The answer to (\partial)/(\partial x)((ln(1+e^{(x)}))^2) is (2e^xln(1+e^x))/(1+e^x)