What is the derivative of y=((2x^2)/(6-x))^3 ?

The derivative of y=((2x^2)/(6-x))^3 is (24x^4(12x-x^2))/((6-x)^4)

What is the first derivative of y=((2x^2)/(6-x))^3 ?

The first derivative of y=((2x^2)/(6-x))^3 is (24x^4(12x-x^2))/((6-x)^4)

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derivative of

y = (\frac{2 x ^{2}}{6 - x})^{3}

\frac{24 x ^{4} ( 12 x - x ^{2} )}{( 6 - x ) ^{4}}

Solution steps

\frac{d}{d x} ((\frac{2 x ^{2}}{6 - x})^{3})

Apply the chain rule:

3 (\frac{2 x ^{2}}{6 - x})^{2} \frac{d}{d x} (\frac{2 x ^{2}}{6 - x})

= 3 (\frac{2 x ^{2}}{6 - x})^{2} \frac{d}{d x} (\frac{2 x ^{2}}{6 - x})

\frac{d}{d x} (\frac{2 x ^{2}}{6 - x}) = \frac{2 ( 12 x - x ^{2} )}{( 6 - x ) ^{2}}

= 3 (\frac{2 x ^{2}}{6 - x})^{2} \frac{2 ( 12 x - x ^{2} )}{( 6 - x ) ^{2}}

Simplify

3 (\frac{2 x ^{2}}{6 - x})^{2} \frac{2 ( 12 x - x ^{2} )}{( 6 - x ) ^{2}} : \frac{24 x ^{4} ( 12 x - x ^{2} )}{( 6 - x ) ^{4}}

= \frac{24 x ^{4} ( 12 x - x ^{2} )}{( 6 - x ) ^{4}}

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x^{2} - 6, - 2 x + 9, - 5, 3

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What is the derivative of y=((2x^2)/(6-x))^3 ?
The derivative of y=((2x^2)/(6-x))^3 is (24x^4(12x-x^2))/((6-x)^4)
What is the first derivative of y=((2x^2)/(6-x))^3 ?
The first derivative of y=((2x^2)/(6-x))^3 is (24x^4(12x-x^2))/((6-x)^4)