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

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

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

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

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derivative of

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

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

Solution steps

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{\partial}{\partial y} (5 x + y)

\frac{d}{d a} (sin^{4} (a) + cos^{4} (a))

\int \frac{sec ( x ) tan ( x )}{- 5 + sec ( x )} d x

x \to 0 + lim (9 cos (9 x))

\int \frac{e ^{x}}{e ^{x} - 2} d x

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