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Popular >

derivative of 1/3 ln(e^x+1)

Solution

\frac{d}{d x} (\frac{1}{3} ln (e^{x} + 1))

Solution

\frac{e ^{x}}{3 ( e ^{x} + 1 )}

Solution steps

\frac{d}{d x} (\frac{1}{3} ln (e^{x} + 1))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{3} \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}{3} \cdot \frac{1}{e ^{x} + 1} e^{x}

Simplify

\frac{1}{3} \cdot \frac{1}{e ^{x} + 1} e^{x} : \frac{e ^{x}}{3 ( e ^{x} + 1 )}

= \frac{e ^{x}}{3 ( e ^{x} + 1 )}

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Frequently Asked Questions (FAQ)

What is the derivative of 1/3 ln(e^x+1) ?
The derivative of 1/3 ln(e^x+1) is (e^x)/(3(e^x+1))
What is the first derivative of 1/3 ln(e^x+1) ?
The first derivative of 1/3 ln(e^x+1) is (e^x)/(3(e^x+1))