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

The derivative of ((4x^2)/(4-x))^3 is (192x^4(8x-x^2))/((4-x)^4)

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

The first derivative of ((4x^2)/(4-x))^3 is (192x^4(8x-x^2))/((4-x)^4)

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derivative of

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

\frac{192 x ^{4} ( 8 x - x ^{2} )}{( 4 - x ) ^{4}}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{4 x ^{2}}{4 - x}) = \frac{4 ( 8 x - x ^{2} )}{( 4 - x ) ^{2}}

= 3 (\frac{4 x ^{2}}{4 - x})^{2} \frac{4 ( 8 x - x ^{2} )}{( 4 - x ) ^{2}}

Simplify

3 (\frac{4 x ^{2}}{4 - x})^{2} \frac{4 ( 8 x - x ^{2} )}{( 4 - x ) ^{2}} : \frac{192 x ^{4} ( 8 x - x ^{2} )}{( 4 - x ) ^{4}}

= \frac{192 x ^{4} ( 8 x - x ^{2} )}{( 4 - x ) ^{4}}

What is the derivative of ((4x^2)/(4-x))^3 ?
The derivative of ((4x^2)/(4-x))^3 is (192x^4(8x-x^2))/((4-x)^4)
What is the first derivative of ((4x^2)/(4-x))^3 ?
The first derivative of ((4x^2)/(4-x))^3 is (192x^4(8x-x^2))/((4-x)^4)