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

The derivative of 1/(x^2sqrt(x)) is -5/(2x^{7/2)}

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

The first derivative of 1/(x^2sqrt(x)) is -5/(2x^{7/2)}

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 ^{2} x})

- \frac{5}{2 x ^{\frac{7}{2}}}

Solution steps

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

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

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

Simplify

- \frac{1}{( x ^{2} x ) ^{2}} \cdot \frac{5 x ^{\frac{3}{2}}}{2} : - \frac{5}{2 x ^{\frac{7}{2}}}

= - \frac{5}{2 x ^{\frac{7}{2}}}

\int \frac{1}{( 1 - x ^{2} ) ^{0.5}} d x

\int \frac{x ^{2} - 3}{x ^{8}} d x

\int 2 x^{2} (- x^{3} + 3)^{5} d x

\frac{\partial}{\partial t} (3 arcsin (t))

\frac{d y}{d x} = - (1 + y)^{4}

What is the derivative of 1/(x^2sqrt(x)) ?
The derivative of 1/(x^2sqrt(x)) is -5/(2x^{7/2)}
What is the first derivative of 1/(x^2sqrt(x)) ?
The first derivative of 1/(x^2sqrt(x)) is -5/(2x^{7/2)}