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Popular >

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

Solution

derivative of

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Simplify

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

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

Popular Examples

limit as x approaches 0+of (2^x)/(3^x)

x \to 0 + lim (\frac{2 ^{x}}{3 ^{x}})

integral of ((x+1))/(x^2+2x+8)

\int \frac{( x + 1 )}{x ^{2} + 2 x + 8} d x

integral of x^3e^{x^{4+5}}

\int x^{3} e^{x^{4 + 5}} d x

inverse oflaplace 4/(s*(s^2-4s+5))inverse laplace

\frac{4}{s \cdot ( s ^{2} - 4 s + 5 )}

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

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

Frequently Asked Questions (FAQ)

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