What is the derivative of y= 2/(3sqrt(x^3)) ?

The derivative of y= 2/(3sqrt(x^3)) is -(x^2)/((x^3)^{3/2)}

What is the first derivative of y= 2/(3sqrt(x^3)) ?

The first derivative of y= 2/(3sqrt(x^3)) is -(x^2)/((x^3)^{3/2)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

y = \frac{2}{3 x ^{3}}

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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