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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

integral of ((10)/x+x/(10))

\int (\frac{10}{x} + \frac{x}{10}) d x

limit as x approaches infinity of x^29

x \to \infty lim (x^{2} 9)

integral of (x^2)/((6-x^3)^5)

\int \frac{x ^{2}}{( 6 - x ^{3} ) ^{5}} d x

derivative of y=ln(x/(x^2+1))derivative of

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

derivative of 3^{2x-1}

\frac{d}{d x} (3^{2 x - 1})

Frequently Asked Questions (FAQ)

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