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

The derivative of ((6x^2)/(6-x))^3 is (648x^4(12x-x^2))/((6-x)^4)

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

The first derivative of ((6x^2)/(6-x))^3 is (648x^4(12x-x^2))/((6-x)^4)

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derivative of

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

\frac{648 x ^{4} ( 12 x - x ^{2} )}{( 6 - x ) ^{4}}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

3 (\frac{6 x ^{2}}{6 - x})^{2} \frac{6 ( 12 x - x ^{2} )}{( 6 - x ) ^{2}} : \frac{648 x ^{4} ( 12 x - x ^{2} )}{( 6 - x ) ^{4}}

= \frac{648 x ^{4} ( 12 x - x ^{2} )}{( 6 - x ) ^{4}}

\int \frac{( 1 - x ) y}{x}

x \to 0 lim (∣ 5 x ∣)

\frac{d}{d x} (\frac{1}{3 2 x - 1})

\frac{d}{d x} (x ln (ln (x)))

\int \frac{x ^{2} + 1}{( x + 2 ) ( x ^{2} + 2 x + 5 )} d x

What is the derivative of ((6x^2)/(6-x))^3 ?
The derivative of ((6x^2)/(6-x))^3 is (648x^4(12x-x^2))/((6-x)^4)
What is the first derivative of ((6x^2)/(6-x))^3 ?
The first derivative of ((6x^2)/(6-x))^3 is (648x^4(12x-x^2))/((6-x)^4)