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Popular >

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

Solution

derivative of

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

(dy)/(dt)=sqrt(t)+t^2

\frac{d y}{d t} = t + t^{2}

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

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

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\int 13 - x^{2} d x

(\partial)/(\partial z)(2ysin(x)+e^{2z})

\frac{\partial}{\partial z} (2 y sin (x) + e^{2 z})

integral from 1/5 to 3 of 14xln(5x)

\int_{\frac{1}{5}}^{3} 14 x ln (5 x) d x

Frequently Asked Questions (FAQ)

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