What is the derivative of (5x^2/((x^2+x)^3)) ?

The derivative of (5x^2/((x^2+x)^3)) is (5(-4x-1))/(x^2(x+1)^4)

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

The first derivative of (5x^2/((x^2+x)^3)) is (5(-4x-1))/(x^2(x+1)^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{5 x ^{2}}{( x ^{2} + x ) ^{3}})

\frac{5 ( - 4 x - 1 )}{x ^{2} ( x + 1 ) ^{4}}

Solution steps

\frac{d}{d x} (\frac{5 x ^{2}}{( x ^{2} + x ) ^{3}})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 5 \frac{d}{d x} (\frac{x ^{2}}{( x ^{2} + x ) ^{3}})

Apply the Quotient Rule:

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

= 5 \cdot \frac{\frac{d}{d x} ( x ^{2} ) ( x ^{2} + x ) ^{3} - \frac{d}{d x} ( ( x ^{2} + x ) ^{3} ) x ^{2}}{( ( x ^{2} + x ) ^{3} ) ^{2}}

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

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

= 5 \cdot \frac{2 x ( x ^{2} + x ) ^{3} - 3 ( x ^{2} + x ) ^{2} ( 2 x + 1 ) x ^{2}}{( ( x ^{2} + x ) ^{3} ) ^{2}}

Simplify

5 \cdot \frac{2 x ( x ^{2} + x ) ^{3} - 3 ( x ^{2} + x ) ^{2} ( 2 x + 1 ) x ^{2}}{( ( x ^{2} + x ) ^{3} ) ^{2}} : \frac{5 ( - 4 x - 1 )}{x ^{2} ( x + 1 ) ^{4}}

= \frac{5 ( - 4 x - 1 )}{x ^{2} ( x + 1 ) ^{4}}

(- 3, - 1), (2, - 2)

h (x) = \frac{1}{x - 2}, (3, 1)

\int \frac{2 x y}{( x ^{2} + y ^{2} ) ^{2}} d x

\int \frac{4}{x} d x

\frac{d ^{2}}{d x ^{2}} (f (x) g (x))

What is the derivative of (5x^2/((x^2+x)^3)) ?
The derivative of (5x^2/((x^2+x)^3)) is (5(-4x-1))/(x^2(x+1)^4)
What is the first derivative of (5x^2/((x^2+x)^3)) ?
The first derivative of (5x^2/((x^2+x)^3)) is (5(-4x-1))/(x^2(x+1)^4)