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

The derivative of (ln(1+x)/x) is (x-ln(1+x)(1+x))/(x^2(1+x))

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

x \to 0 lim (h (x) (x^{\frac{2}{3}}))

y = x^{3} - x, y = 5 x

\frac{d}{d x} (3^{(x^{5})})

\int_{0}^{1} \frac{1}{9 - x ^{2}} d x

\frac{\partial}{\partial x} (tan (x) arcsin (x))

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