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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\frac{d}{d x} ((\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_{0}^{2} (2 - x)^{2} d x

cos (x)

3 x^{2}, 18 x - 6 x^{2}

\int_{1}^{3} 2 x^{2} - 2 x + 3 d x

\int_{0}^{1} (sin (2 π t))^{2} d t

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)