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

The derivative of ((2x^2/(4-x))^3) is (24x^4(8x-x^2))/((4-x)^4)

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

The first derivative of ((2x^2/(4-x))^3) is (24x^4(8x-x^2))/((4-x)^4)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

\frac{24 x ^{4} ( 8 x - x ^{2} )}{( 4 - x ) ^{4}}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

3 (\frac{2 x ^{2}}{4 - x})^{2} \frac{2 ( 8 x - x ^{2} )}{( 4 - x ) ^{2}} : \frac{24 x ^{4} ( 8 x - x ^{2} )}{( 4 - x ) ^{4}}

= \frac{24 x ^{4} ( 8 x - x ^{2} )}{( 4 - x ) ^{4}}

\int \frac{3}{x ^{2} + 4 x - 5} d x

x \to 0 + lim ((1 + x)^{\frac{2}{x}})

f (x) = e^{x^{5} + 2 x}

y = x^{2} y^{3} + x^{3} y^{2}

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

What is the derivative of ((2x^2/(4-x))^3) ?
The derivative of ((2x^2/(4-x))^3) is (24x^4(8x-x^2))/((4-x)^4)
What is the first derivative of ((2x^2/(4-x))^3) ?
The first derivative of ((2x^2/(4-x))^3) is (24x^4(8x-x^2))/((4-x)^4)