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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int - 2 ln (x^{2} - 1) d x

f (x) = 11 x - 1

x \to 4 lim ((3 x - 3)^{\frac{5}{2}})

\int \frac{( 14 x ^{3} + 2 x + 1 )}{x ^{3}} d x

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

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