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))

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derivative of

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

\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 )}

\frac{d}{d x} ((\frac{x}{( y + z )})^{2})

x^{3} + 3 x^{2} + 5

f (x) = 2 cos (2 x - 1)

\frac{- 1}{sin ^{2} ( x )}

\frac{d}{d v} (\frac{( v - 0 )}{t})

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))