What is the derivative of ln(1+e^{2x}) ?

The derivative of ln(1+e^{2x}) is (2e^{2x})/(1+e^{2x)}

What is the first derivative of ln(1+e^{2x}) ?

The first derivative of ln(1+e^{2x}) is (2e^{2x})/(1+e^{2x)}

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

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

Solution steps

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

Apply the chain rule:

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

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

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

= \frac{1}{1 + e ^{2 x}} \cdot 2 e^{2 x}

Simplify

\frac{1}{1 + e ^{2 x}} \cdot 2 e^{2 x} : \frac{2 e ^{2 x}}{1 + e ^{2 x}}

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

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