What is the derivative of x/((1-x^2^{3/2)}) ?

The derivative of x/((1-x^2^{3/2)}) is (2x^2+1)/((1-x^2)^{5/2)}

What is the first derivative of x/((1-x^2^{3/2)}) ?

The first derivative of x/((1-x^2^{3/2)}) is (2x^2+1)/((1-x^2)^{5/2)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{d}{d x} (\frac{x}{( 1 - x ^{2} ) ^{\frac{3}{2}}})

\frac{2 x ^{2} + 1}{( 1 - x ^{2} ) ^{\frac{5}{2}}}

Solution steps

\frac{d}{d x} (\frac{x}{( 1 - x ^{2} ) ^{\frac{3}{2}}})

Apply the Quotient Rule:

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

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

\frac{d x}{d x} = 1

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

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

Simplify

\frac{1 \cdot ( 1 - x ^{2} ) ^{\frac{3}{2}} - ( - 3 x ( 1 - x ^{2} ) ^{\frac{1}{2}} ) x}{( ( 1 - x ^{2} ) ^{\frac{3}{2}} ) ^{2}} : \frac{2 x ^{2} + 1}{( 1 - x ^{2} ) ^{\frac{5}{2}}}

= \frac{2 x ^{2} + 1}{( 1 - x ^{2} ) ^{\frac{5}{2}}}

\frac{\partial}{\partial x} (e^{5 x e^{y}})

\int_{- 1}^{1} (2 x + 3) d x

\int x^{a} ln (x) d x

\int e^{12 x} d x

π t

What is the derivative of x/((1-x^2^{3/2)}) ?
The derivative of x/((1-x^2^{3/2)}) is (2x^2+1)/((1-x^2)^{5/2)}
What is the first derivative of x/((1-x^2^{3/2)}) ?
The first derivative of x/((1-x^2^{3/2)}) is (2x^2+1)/((1-x^2)^{5/2)}