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

The derivative of (x^2)/(2+sqrt(x)) is (4x(2+sqrt(x))-x^{3/2})/(2(2+sqrt(x))^2)

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

The first derivative of (x^2)/(2+sqrt(x)) is (4x(2+sqrt(x))-x^{3/2})/(2(2+sqrt(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 ( 2 + x ) - x ^{\frac{3}{2}}}{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) = \frac{1}{2 x}

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

Simplify

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

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

\int_{- 1}^{64} \frac{1}{x ^{\frac{1}{3}}} d x

n = 1 \sum \infty \frac{2}{3 ^{n}}

x \to 2 lim (3 + 2 x + x^{2})

x \to 3 lim (\frac{∣ x - 3 ∣}{x + 3})

f (x) = 16 - 7 e^{x}

What is the derivative of (x^2)/(2+sqrt(x)) ?
The derivative of (x^2)/(2+sqrt(x)) is (4x(2+sqrt(x))-x^{3/2})/(2(2+sqrt(x))^2)
What is the first derivative of (x^2)/(2+sqrt(x)) ?
The first derivative of (x^2)/(2+sqrt(x)) is (4x(2+sqrt(x))-x^{3/2})/(2(2+sqrt(x))^2)