What is the (x/(3x+4ln(x)))^' ?

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

What is the first (x/(3x+4ln(x)))^' ?

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

x^{'} = 1

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

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

Simplify

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

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

\frac{\partial}{\partial x} (5 - 3 x)

f (x) = sin^{3} (2 x)

\frac{s - 10}{s ^{3} ( s + 2.5 ) ^{2}}

\frac{\partial ^{2}}{\partial x \partial y} (x y e^{- 7 y})

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

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