What is the derivative of f(x)= 1/(sqrt(x^5)) ?

The derivative of f(x)= 1/(sqrt(x^5)) is -(5x^4)/(2(x^5)^{3/2)}

What is the first derivative of f(x)= 1/(sqrt(x^5)) ?

The first derivative of f(x)= 1/(sqrt(x^5)) is -(5x^4)/(2(x^5)^{3/2)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

f (x) = \frac{1}{x ^{5}}

- \frac{5 x ^{4}}{2 ( x ^{5} ) ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (\frac{1}{x ^{5}})

Apply exponent rule:

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (x^{5}) = 5 x^{4}

= - \frac{1}{2 ( x ^{5} ) ^{\frac{3}{2}}} \cdot 5 x^{4}

Simplify

- \frac{1}{2 ( x ^{5} ) ^{\frac{3}{2}}} \cdot 5 x^{4} : - \frac{5 x ^{4}}{2 ( x ^{5} ) ^{\frac{3}{2}}}

= - \frac{5 x ^{4}}{2 ( x ^{5} ) ^{\frac{3}{2}}}

What is the derivative of f(x)= 1/(sqrt(x^5)) ?
The derivative of f(x)= 1/(sqrt(x^5)) is -(5x^4)/(2(x^5)^{3/2)}
What is the first derivative of f(x)= 1/(sqrt(x^5)) ?
The first derivative of f(x)= 1/(sqrt(x^5)) is -(5x^4)/(2(x^5)^{3/2)}