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 \frac{x ^{2}}{3 + x} d x

\frac{\partial}{\partial x} (3 x y z^{2})

s + 1

\int (4 x + 1)^{5} d x

x + 9

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)