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Popular >

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

Solution

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

Solution

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

Solution steps

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

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

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

Popular Examples

integral of 1/(5+x)

\int \frac{1}{5 + x} d x

sin(2x)dx+cos(5y)dy=0,y(pi/2)= pi/5

sin (2 x) d x + cos (5 y) d y = 0, y (\frac{π}{2}) = \frac{π}{5}

y^{''''}+20y^{''}+100y=0

y^{^{''''}} + 20 y^{^{''}} + 100 y = 0

derivative of 10x(x^2+3^4)

\frac{d}{d x} (10 x (x^{2} + 3)^{4})

derivative of-46xsin(x^2)derivative of

- 46 x sin (x^{2})

Frequently Asked Questions (FAQ)

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