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Popular >

derivative of x^{-2}ln(x)

Solution

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

Solution

\frac{- 2 ln ( x ) + 1}{x ^{3}}

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{- 2}, g = ln (x)

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

\frac{d}{d x} (x^{- 2}) = - \frac{2}{x ^{3}}

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

= (- \frac{2}{x ^{3}}) ln (x) + \frac{1}{x} x^{- 2}

Simplify

(- \frac{2}{x ^{3}}) ln (x) + \frac{1}{x} x^{- 2} : \frac{- 2 ln ( x ) + 1}{x ^{3}}

= \frac{- 2 ln ( x ) + 1}{x ^{3}}

Popular Examples

integral from 1 to 4 of x/(x^2+6x+13)

\int_{1}^{4} \frac{x}{x ^{2} + 6 x + 13} d x

(\partial)/(\partial x)(arctan(3x))

\frac{\partial}{\partial x} (arctan (3 x))

limit as x approaches infinity of (sqrt(4x^6-x))/(x^3+2)

x \to \infty lim (\frac{4 x ^{6} - x}{x ^{3} + 2})

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x \to \infty lim (2 x e^{- 2 x})

derivative of g(x)=x(x-4)^3 derivative of

g (x) = x (x - 4)^{3}

Frequently Asked Questions (FAQ)

What is the derivative of x^{-2}ln(x) ?
The derivative of x^{-2}ln(x) is (-2ln(x)+1)/(x^3)
What is the first derivative of x^{-2}ln(x) ?
The first derivative of x^{-2}ln(x) is (-2ln(x)+1)/(x^3)