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

The derivative of (2+x/((2-x)^5)) is (4(x+3))/((2-x)^6)

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

The first derivative of (2+x/((2-x)^5)) is (4(x+3))/((2-x)^6)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

\frac{4 ( x + 3 )}{( 2 - x ) ^{6}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

= \frac{4 ( x + 3 )}{( 2 - x ) ^{6}}

What is the derivative of (2+x/((2-x)^5)) ?
The derivative of (2+x/((2-x)^5)) is (4(x+3))/((2-x)^6)
What is the first derivative of (2+x/((2-x)^5)) ?
The first derivative of (2+x/((2-x)^5)) is (4(x+3))/((2-x)^6)