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

The derivative of (x^3)/(3-3x) is (x^2(-2x+3))/(3(x-1)^2)

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

The first derivative of (x^3)/(3-3x) is (x^2(-2x+3))/(3(x-1)^2)

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derivative of

\frac{x ^{3}}{3 - 3 x}

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

Solution steps

\frac{d}{d x} (\frac{x ^{3}}{3 - 3 x})

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

d er i v a t i v e 3^{x} + 2

d er i v a t i v e lo g_{10} (\frac{2}{x})

d er i v a t i v e \frac{( 3 x ^{2} - 1 ) ^{2}}{( x + 1 ) ^{3}}

d er i v a t i v e 1 4^{x} + 16

d er i v a t i v e \frac{2 x - 3}{x}

What is the derivative of (x^3)/(3-3x) ?
The derivative of (x^3)/(3-3x) is (x^2(-2x+3))/(3(x-1)^2)
What is the first derivative of (x^3)/(3-3x) ?
The first derivative of (x^3)/(3-3x) is (x^2(-2x+3))/(3(x-1)^2)