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Popular >

derivative of ln^2(x+2ln(x))

Solution

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

Solution

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

\frac{d}{d x} (ln^{2} (x)) = \frac{2 ln ( x )}{x}

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

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

Apply rule

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

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

Popular Examples

integral of 1/(x^2(sqrt(x^2-16)))

\int \frac{1}{x ^{2} ( x ^{2} - 16 )} d x

integral of ln(cos(x))tan(x)

\int ln (cos (x)) tan (x) d x

(dy)/(dx)=(-24)/((2x+9)^3)

\frac{d y}{d x} = \frac{- 24}{( 2 x + 9 ) ^{3}}

(\partial)/(\partial y)(e^{-y}cos(pix))

\frac{\partial}{\partial y} (e^{- y} cos (π x))

integral of (x^2+e^x-sin(x))

\int (x^{2} + e^{x} - sin (x)) d x

Frequently Asked Questions (FAQ)

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