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Popular >

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

Solution

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

Solution

\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}}

Graph

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\int_{2}^{\infty} \frac{1}{x ^{2} - 1} d x

(dy)/(dx)+y=y^2,y(0)=2

\frac{d y}{d x} + y = y^{2}, y (0) = 2

integral of sqrt(y/4)

\int \frac{y}{4} d y

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Frequently Asked Questions (FAQ)

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)}