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Popular >

derivative of (ln(x+1)/x)

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

\frac{d}{d x} (ln (x + 1)) = \frac{1}{x + 1}

\frac{d x}{d x} = 1

= \frac{\frac{1}{x + 1} x - 1 \cdot ln ( x + 1 )}{x ^{2}}

Simplify

\frac{\frac{1}{x + 1} x - 1 \cdot ln ( x + 1 )}{x ^{2}} : \frac{x - ln ( x + 1 ) ( x + 1 )}{x ^{2} ( x + 1 )}

= \frac{x - ln ( x + 1 ) ( x + 1 )}{x ^{2} ( x + 1 )}

Graph

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Frequently Asked Questions (FAQ)

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