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

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

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

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

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derivative of

ln (1 + e^{x})

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{5 x}{x + 4}

\frac{d}{d x} (\frac{3}{tan ( x )})

x \to 1 lim (\frac{∣ x + 1 ∣}{x + 1})

\frac{\partial}{\partial y} (ln (x) y)

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