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Popular >

derivative of y=(ln(x))/x

Solution

derivative of

y = \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

(\partial)/(\partial x)(Asqrt(x/z))

\frac{\partial}{\partial x} (A \frac{x}{z})

derivative of (3x-4/((5x+2)^3))

\frac{d}{d x} (\frac{3 x - 4}{( 5 x + 2 ) ^{3}})

integral from 0 to 3 of 1/(sqrt(36-x^2))

\int_{0}^{3} \frac{1}{36 - x ^{2}} d x

derivative of f(x)=(6x+2)^3 derivative of

f (x) = (6 x + 2)^{3}

integral of-x/(x-1)

\int - \frac{x}{x - 1} d x

Frequently Asked Questions (FAQ)

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