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Popular >

derivative of (ln(4x))/x

Solution

derivative of

\frac{ln ( 4 x )}{x}

Solution

\frac{1 - ln ( 4 x )}{x ^{2}}

Solution steps

\frac{d}{d x} (\frac{ln ( 4 x )}{x})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( ln ( 4 x ) ) x - \frac{d x}{d x} ln ( 4 x )}{x ^{2}}

\frac{d}{d x} (ln (4 x)) = \frac{1}{x}

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

= \frac{\frac{1}{x} x - 1 \cdot ln ( 4 x )}{x ^{2}}

Simplify

\frac{\frac{1}{x} x - 1 \cdot ln ( 4 x )}{x ^{2}} : \frac{1 - ln ( 4 x )}{x ^{2}}

= \frac{1 - ln ( 4 x )}{x ^{2}}

Popular Examples

(\partial}{\partial t}(\frac{(2r+s))/t)

\frac{\partial}{\partial t} (\frac{( 2 r + s )}{t})

limit as x approaches 0 of 2(tan(x))^x

x \to 0 lim (2 (tan (x))^{x})

integral of x^2e^{22x}

\int x^{2} e^{22 x} d x

derivative of y=(x^3+1)/(x^2-1)derivative of

y = \frac{x ^{3} + 1}{x ^{2} - 1}

derivative of f(x)=(x^2)/(x^2+2)derivative of

f (x) = \frac{x ^{2}}{x ^{2} + 2}

Frequently Asked Questions (FAQ)

What is the derivative of (ln(4x))/x ?
The derivative of (ln(4x))/x is (1-ln(4x))/(x^2)
What is the first derivative of (ln(4x))/x ?
The first derivative of (ln(4x))/x is (1-ln(4x))/(x^2)