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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Graph

Popular Examples

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\frac{d}{d x} (4 x e^{- 2 x} cos (4 π x + 30))

integral of 6x+1/(x^2)

\int 6 x + \frac{1}{x ^{2}} d x

derivative of (x^2+2x-2/((x+1)^2))

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

limit as x approaches 1+of 2x-3

x \to 1 + lim (2 x - 3)

integral from ln(2) to ln(4) of e^{-x}

\int_{l n (2)}^{l n (4)} e^{- x} d x

Frequently Asked Questions (FAQ)

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