What is the derivative of ((x^2))/(8+x) ?

The derivative of ((x^2))/(8+x) is (16x+x^2)/((8+x)^2)

What is the first derivative of ((x^2))/(8+x) ?

The first derivative of ((x^2))/(8+x) is (16x+x^2)/((8+x)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

\frac{( x ^{2} )}{8 + x}

\frac{16 x + x ^{2}}{( 8 + x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{2}}{8 + x})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ^{2} ) ( 8 + x ) - \frac{d}{d x} ( 8 + x ) x ^{2}}{( 8 + x ) ^{2}}

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

\frac{d}{d x} (8 + x) = 1

= \frac{2 x ( 8 + x ) - 1 \cdot x ^{2}}{( 8 + x ) ^{2}}

Simplify

\frac{2 x ( 8 + x ) - 1 \cdot x ^{2}}{( 8 + x ) ^{2}} : \frac{16 x + x ^{2}}{( 8 + x ) ^{2}}

= \frac{16 x + x ^{2}}{( 8 + x ) ^{2}}

y = x^{2}, y = 2 - x^{2}

e^{x^{5}}

y = \frac{x}{x}

t^{2} y^{^{''}} + 17 t y^{^{'}} + 64 y = 0

What is the derivative of ((x^2))/(8+x) ?
The derivative of ((x^2))/(8+x) is (16x+x^2)/((8+x)^2)
What is the first derivative of ((x^2))/(8+x) ?
The first derivative of ((x^2))/(8+x) is (16x+x^2)/((8+x)^2)