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Popular >

derivative of ln((x+2/(x+1)))

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

integral of (a+bx^8)/(sqrt(9ax+bx^9))

\int \frac{a + b x ^{8}}{9 a x + b x ^{9}} d x

limit as x approaches infinity of b^x

x \to \infty lim (b^{x})

laplacetransform cos(t-pi/6)laplace transform

cos (t - \frac{π}{6})

integral of-cos(x)+sin(x)

\int - cos (x) + sin (x) d x

derivative of 2/3 x

\frac{d}{d x} (\frac{2}{3} x)

Frequently Asked Questions (FAQ)

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