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

The derivative of (4x^3)/(3-x) is (4(9x^2-2x^3))/((3-x)^2)

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

The first derivative of (4x^3)/(3-x) is (4(9x^2-2x^3))/((3-x)^2)

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derivative of

\frac{4 x ^{3}}{3 - x}

\frac{4 ( 9 x ^{2} - 2 x ^{3} )}{( 3 - x ) ^{2}}

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 4 \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}}

= 4 \cdot \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

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

Simplify

4 \cdot \frac{3 x ^{2} ( 3 - x ) - ( - 1 ) x ^{3}}{( 3 - x ) ^{2}} : \frac{4 ( 9 x ^{2} - 2 x ^{3} )}{( 3 - x ) ^{2}}

= \frac{4 ( 9 x ^{2} - 2 x ^{3} )}{( 3 - x ) ^{2}}

3 x^{2} + 5 x - 5

y = 3 x (4 x - 5) 2

y = 7 x^{6}

x^{3} + 3 x + 5

x^{3} y^{3}

What is the derivative of (4x^3)/(3-x) ?
The derivative of (4x^3)/(3-x) is (4(9x^2-2x^3))/((3-x)^2)
What is the first derivative of (4x^3)/(3-x) ?
The first derivative of (4x^3)/(3-x) is (4(9x^2-2x^3))/((3-x)^2)