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Popular >

derivative of (ln(x))/x

Solution

derivative of

\frac{ln ( x )}{x}

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

Popular Examples

integral of (x^2-3x-10)/(x+2)

\int \frac{x ^{2} - 3 x - 10}{x + 2} d x

limit as x approaches 0+of xcos(3/x)

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

limit as x approaches 1+of 2x-1

x \to 1 + lim (2 x - 1)

derivative of 3xln(x)

\frac{d}{d x} (3 x ln (x))

sum from n=1 to infinity of 2-8(0.9)^n

n = 1 \sum \infty 2 - 8 (0.9)^{n}

Frequently Asked Questions (FAQ)

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