What is the derivative of x/(4x-3ln(x)) ?

The derivative of x/(4x-3ln(x)) is (-3ln(x)+3)/((4x-3ln(x))^2)

What is the first derivative of x/(4x-3ln(x)) ?

The first derivative of x/(4x-3ln(x)) is (-3ln(x)+3)/((4x-3ln(x))^2)

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\frac{d}{d x} (\frac{x}{4 x - 3 ln ( x )})

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

Solution steps

\frac{d}{d x} (\frac{x}{4 x - 3 ln ( x )})

Apply the Quotient Rule:

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

= \frac{\frac{d x}{d x} ( 4 x - 3 ln ( x ) ) - \frac{d}{d x} ( 4 x - 3 ln ( x ) ) x}{( 4 x - 3 ln ( x ) ) ^{2}}

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

\frac{d}{d x} (4 x - 3 ln (x)) = 4 - \frac{3}{x}

= \frac{1 \cdot ( 4 x - 3 ln ( x ) ) - ( 4 - \frac{3}{x} ) x}{( 4 x - 3 ln ( x ) ) ^{2}}

Simplify

\frac{1 \cdot ( 4 x - 3 ln ( x ) ) - ( 4 - \frac{3}{x} ) x}{( 4 x - 3 ln ( x ) ) ^{2}} : \frac{- 3 ln ( x ) + 3}{( 4 x - 3 ln ( x ) ) ^{2}}

= \frac{- 3 ln ( x ) + 3}{( 4 x - 3 ln ( x ) ) ^{2}}

\int x (sin (x)) d x

x \to 0 lim (\frac{x}{∣ x ∣ + x})

n = 1 \sum \infty \frac{1}{10 n + 1}

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

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

What is the derivative of x/(4x-3ln(x)) ?
The derivative of x/(4x-3ln(x)) is (-3ln(x)+3)/((4x-3ln(x))^2)
What is the first derivative of x/(4x-3ln(x)) ?
The first derivative of x/(4x-3ln(x)) is (-3ln(x)+3)/((4x-3ln(x))^2)