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

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

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

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

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

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = \frac{1}{x}, g = x^{2} - \frac{2}{x}

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

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

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

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

Simplify

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

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

\frac{d}{d x} (- \frac{4 x}{( x ^{2} - 4 ) ^{2}})

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

\frac{A}{y ^{7}} + B e^{y}

n = 1 \sum \infty \frac{3 - 2 n}{4 n}

(- 2, 7), (2, 3)

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