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

The derivative of (x^3)/(3-x) is (9x^2-2x^3)/((3-x)^2)

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

The first derivative of (x^3)/(3-x) is (9x^2-2x^3)/((3-x)^2)

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derivative of

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

\frac{9 x ^{2} - 2 x ^{3}}{( 3 - x ) ^{2}}

Solution steps

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

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

\frac{d}{d x} (3 - x) = - 1

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

Simplify

\frac{3 x ^{2} ( 3 - x ) - ( - 1 ) x ^{3}}{( 3 - x ) ^{2}} : \frac{9 x ^{2} - 2 x ^{3}}{( 3 - x ) ^{2}}

= \frac{9 x ^{2} - 2 x ^{3}}{( 3 - x ) ^{2}}

\frac{1}{( 1 + e ^{- x} )}

cos^{5} (x) + tan^{5} (x)

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

\frac{d}{d x} (1.2 \cdot sin (2 \cdot x - 0.8 \cdot t + 10))

\frac{ln ( x )}{2}

What is the derivative of (x^3)/(3-x) ?
The derivative of (x^3)/(3-x) is (9x^2-2x^3)/((3-x)^2)
What is the first derivative of (x^3)/(3-x) ?
The first derivative of (x^3)/(3-x) is (9x^2-2x^3)/((3-x)^2)