What is the derivative of-(36(x-1))/((x+3)^3) ?

The derivative of-(36(x-1))/((x+3)^3) is -(72(-x+3))/((x+3)^4)

What is the first derivative of-(36(x-1))/((x+3)^3) ?

The first derivative of-(36(x-1))/((x+3)^3) is -(72(-x+3))/((x+3)^4)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

- \frac{36 ( x - 1 )}{( x + 3 ) ^{3}}

- \frac{72 ( - x + 3 )}{( x + 3 ) ^{4}}

Solution steps

\frac{d}{d x} (- \frac{36 ( x - 1 )}{( x + 3 ) ^{3}})

Take the constant out:

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

= - 36 \frac{d}{d x} (\frac{x - 1}{( x + 3 ) ^{3}})

Apply the Quotient Rule:

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

= - 36 \cdot \frac{\frac{d}{d x} ( x - 1 ) ( x + 3 ) ^{3} - \frac{d}{d x} ( ( x + 3 ) ^{3} ) ( x - 1 )}{( ( x + 3 ) ^{3} ) ^{2}}

\frac{d}{d x} (x - 1) = 1

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

= - 36 \cdot \frac{1 \cdot ( x + 3 ) ^{3} - 3 ( x + 3 ) ^{2} ( x - 1 )}{( ( x + 3 ) ^{3} ) ^{2}}

Simplify

- 36 \cdot \frac{1 \cdot ( x + 3 ) ^{3} - 3 ( x + 3 ) ^{2} ( x - 1 )}{( ( x + 3 ) ^{3} ) ^{2}} : - \frac{72 ( - x + 3 )}{( x + 3 ) ^{4}}

= - \frac{72 ( - x + 3 )}{( x + 3 ) ^{4}}

2 x^{2} + 5, - 2, 3

\int sin (3 θ) d θ

\frac{( 1 - 4 t )}{( 6 + t )}

\frac{d}{d t} (6)

\frac{d}{d x} (- 5 x e^{- x})

What is the derivative of-(36(x-1))/((x+3)^3) ?
The derivative of-(36(x-1))/((x+3)^3) is -(72(-x+3))/((x+3)^4)
What is the first derivative of-(36(x-1))/((x+3)^3) ?
The first derivative of-(36(x-1))/((x+3)^3) is -(72(-x+3))/((x+3)^4)