What is the derivative of (i*(sqrt(x^{-5)})^5) ?

The derivative of (i*(sqrt(x^{-5)})^5) is -(25i)/(2x^{27/2)}

What is the first derivative of (i*(sqrt(x^{-5)})^5) ?

The first derivative of (i*(sqrt(x^{-5)})^5) is -(25i)/(2x^{27/2)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{d}{d x} ((i) \cdot (x^{- 5})^{5})

- \frac{25 i}{2 x ^{\frac{27}{2}}}

Solution steps

\frac{d}{d x} ((i) (x^{- 5})^{5})

Take the constant out:

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (x^{- 5}) = - \frac{5}{2 x ^{\frac{7}{2}}}

= i 5 (x^{- 5})^{4} (- \frac{5}{2 x ^{\frac{7}{2}}})

Simplify

i 5 (x^{- 5})^{4} (- \frac{5}{2 x ^{\frac{7}{2}}}) : - \frac{25 i}{2 x ^{\frac{27}{2}}}

= - \frac{25 i}{2 x ^{\frac{27}{2}}}

e^{2 x - y + z}

\frac{d}{d a} (\frac{a}{18})

e^{s} in x + x (tan (x))^{2}

(4 x + 8)^{\frac{1}{3}}

e^{x} + 2 y

What is the derivative of (i*(sqrt(x^{-5)})^5) ?
The derivative of (i*(sqrt(x^{-5)})^5) is -(25i)/(2x^{27/2)}
What is the first derivative of (i*(sqrt(x^{-5)})^5) ?
The first derivative of (i*(sqrt(x^{-5)})^5) is -(25i)/(2x^{27/2)}