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

The derivative of ((3x^2)/((2x+4)))^3 is (81x^5(x+4))/(2(2x+4)^2(x+2)^2)

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

The first derivative of ((3x^2)/((2x+4)))^3 is (81x^5(x+4))/(2(2x+4)^2(x+2)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

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

\frac{81 x ^{5} ( x + 4 )}{2 ( 2 x + 4 ) ^{2} ( x + 2 ) ^{2}}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

3 (\frac{3 x ^{2}}{2 x + 4})^{2} \frac{3 x ( x + 4 )}{2 ( x + 2 ) ^{2}} : \frac{81 x ^{5} ( x + 4 )}{2 ( 2 x + 4 ) ^{2} ( x + 2 ) ^{2}}

= \frac{81 x ^{5} ( x + 4 )}{2 ( 2 x + 4 ) ^{2} ( x + 2 ) ^{2}}

\frac{d y}{d x} = \frac{( 2 y + 5 ) ^{2}}{( 8 x + 9 ) ^{2}}

y = x^{2}, (2, 4)

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

x^{5} cos (x^{3})

What is the derivative of ((3x^2)/((2x+4)))^3 ?
The derivative of ((3x^2)/((2x+4)))^3 is (81x^5(x+4))/(2(2x+4)^2(x+2)^2)
What is the first derivative of ((3x^2)/((2x+4)))^3 ?
The first derivative of ((3x^2)/((2x+4)))^3 is (81x^5(x+4))/(2(2x+4)^2(x+2)^2)