What is the derivative of 1/(sqrt(x^9)) ?

The derivative of 1/(sqrt(x^9)) is -(9x^8)/(2(x^9)^{3/2)}

What is the first derivative of 1/(sqrt(x^9)) ?

The first derivative of 1/(sqrt(x^9)) is -(9x^8)/(2(x^9)^{3/2)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

\frac{1}{x ^{9}}

- \frac{9 x ^{8}}{2 ( x ^{9} ) ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (\frac{1}{x ^{9}})

Apply exponent rule:

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

= \frac{d}{d x} ((x^{9})^{- \frac{1}{2}})

Apply the chain rule:

- \frac{1}{2 ( x ^{9} ) ^{\frac{3}{2}}} \frac{d}{d x} (x^{9})

= - \frac{1}{2 ( x ^{9} ) ^{\frac{3}{2}}} \frac{d}{d x} (x^{9})

\frac{d}{d x} (x^{9}) = 9 x^{8}

= - \frac{1}{2 ( x ^{9} ) ^{\frac{3}{2}}} \cdot 9 x^{8}

Simplify

- \frac{1}{2 ( x ^{9} ) ^{\frac{3}{2}}} \cdot 9 x^{8} : - \frac{9 x ^{8}}{2 ( x ^{9} ) ^{\frac{3}{2}}}

= - \frac{9 x ^{8}}{2 ( x ^{9} ) ^{\frac{3}{2}}}

What is the derivative of 1/(sqrt(x^9)) ?
The derivative of 1/(sqrt(x^9)) is -(9x^8)/(2(x^9)^{3/2)}
What is the first derivative of 1/(sqrt(x^9)) ?
The first derivative of 1/(sqrt(x^9)) is -(9x^8)/(2(x^9)^{3/2)}