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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

Simplify

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

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

Graph

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Frequently Asked Questions (FAQ)

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