What is the derivative of (x^2)/((3+x)) ?

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

What is the first derivative of (x^2)/((3+x)) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\int \frac{1}{9 x + 4} d x

\int \frac{3 x + 1}{x ^{\frac{2}{3}}} d x

a re a y = 1 - x^{2}, y = 11 - 7 x

\int_{0}^{\frac{π}{2}} - 4 sin^{2} (3 x) d x

\int \frac{1}{x ^{2}} d x

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