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

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

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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

\frac{x ^{2} + 3}{2 x ^{\frac{5}{2}}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

= \frac{x ^{2} + 3}{2 x ^{\frac{5}{2}}}

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