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Popular >

derivative of x-2sqrt(x)+2ln(sqrt(x+1))

Solution

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

Solution

1 - \frac{1}{x} + \frac{1}{x + 1}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

\frac{d x}{d x} = 1

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

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

= 1 - \frac{1}{x} + \frac{1}{x + 1}

Popular Examples

tangent of y= 5/(sqrt(x-2)),(3,5)tangent of

y = \frac{5}{x - 2}, (3, 5)

integral from 0 to 1 of (x^2)/((x+1)^3)

\int_{0}^{1} \frac{x ^{2}}{( x + 1 ) ^{3}} d x

y^'-1/x y=-(y^2)/x

y^{^{'}} - \frac{1}{x} y = - \frac{y ^{2}}{x}

integral of 10m^{-2.3}+5m^{3.6}

\int 10 m^{- 2.3} + 5 m^{3.6} d m

integral of 1/(u^2-1)

\int \frac{1}{u ^{2} - 1} d u

Frequently Asked Questions (FAQ)

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