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

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

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

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

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derivative of

ln (e^{x} + 1)

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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

\int_{0}^{x} sin (x) d x

\frac{\partial}{\partial x} (2 y x^{2} - 3)

f (x) = x^{2} - 3 x + 2

\int_{0}^{1} 7 x e^{- x^{2}} d x

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