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

The derivative of (x^3/((x+2)^2)) is (x^2(x+6))/((x+2)^3)

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

The first derivative of (x^3/((x+2)^2)) is (x^2(x+6))/((x+2)^3)

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{x ^{3}}{( x + 2 ) ^{2}})

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

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Simplify

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

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

\int 36 (4 x + 4)^{(2)} - 2 (3 x - 1) d x

\int cos^{- 1} (x) d x

x^{2} + 9

\int_{1}^{5} \frac{x ^{2} + 8}{6 x - x ^{2}} d x

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

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