What is the derivative of (x^2)/((5+x)^4) ?

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

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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} ((5 + x)^{4}) = 4 (5 + x)^{3}

= \frac{2 x ( 5 + x ) ^{4} - 4 ( 5 + x ) ^{3} x ^{2}}{( ( 5 + x ) ^{4} ) ^{2}}

Simplify

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

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

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