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

The derivative of ((x+1^2(x-5))/((x-1)^3)) is (24(x+1))/((x-1)^4)

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

The first derivative of ((x+1^2(x-5))/((x-1)^3)) is (24(x+1))/((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{( x + 1 ) ^{2} ( x - 5 )}{( x - 1 ) ^{3}})

\frac{24 ( x + 1 )}{( x - 1 ) ^{4}}

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} ((x + 1)^{2} (x - 5)) = 3 x^{2} - 6 x - 9

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

= \frac{( 3 x ^{2} - 6 x - 9 ) ( x - 1 ) ^{3} - 3 ( x - 1 ) ^{2} ( x + 1 ) ^{2} ( x - 5 )}{( ( x - 1 ) ^{3} ) ^{2}}

Simplify

\frac{( 3 x ^{2} - 6 x - 9 ) ( x - 1 ) ^{3} - 3 ( x - 1 ) ^{2} ( x + 1 ) ^{2} ( x - 5 )}{( ( x - 1 ) ^{3} ) ^{2}} : \frac{24 ( x + 1 )}{( x - 1 ) ^{4}}

= \frac{24 ( x + 1 )}{( x - 1 ) ^{4}}

\int 9 e^{3 x} cos (8 x) d x

n = 1 \sum \infty \frac{1}{2 n + 1}

x \to 0 lim (\frac{9 x ^{2} - 6 x}{x})

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

\frac{d}{d x} (a e^{- 3 x})

What is the derivative of ((x+1^2(x-5))/((x-1)^3)) ?
The derivative of ((x+1^2(x-5))/((x-1)^3)) is (24(x+1))/((x-1)^4)
What is the first derivative of ((x+1^2(x-5))/((x-1)^3)) ?
The first derivative of ((x+1^2(x-5))/((x-1)^3)) is (24(x+1))/((x-1)^4)