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

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

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

The first derivative of (x^2)/((2+x)) is (4x+x^2)/((2+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}}{( 2 + x )}

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

y^{^{''}} - 8 y^{^{'}} - 17 y = 0

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

\int_{0}^{\frac{π}{4}} 2 tan^{5} (x) d x

x^{2} - 2 x + 42

\frac{1}{7} x, 7 x^{2}

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