en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of 2/(\sqrt[5]{x^2})

Solution

Solution

- \frac{4}{5 x ^{\frac{7}{5}}}

Solution steps

Take the constant out:

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

Apply exponent rule:

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

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

Apply the chain rule:

- \frac{1}{5 ( x ^{2} ) ^{\frac{6}{5}}} \frac{d}{d x} (x^{2})

= - \frac{1}{5 ( x ^{2} ) ^{\frac{6}{5}}} \frac{d}{d x} (x^{2})

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

= 2 (- \frac{1}{5 ( x ^{2} ) ^{\frac{6}{5}}} \cdot 2 x)

Simplify

2 (- \frac{1}{5 ( x ^{2} ) ^{\frac{6}{5}}} \cdot 2 x) : - \frac{4}{5 x ^{\frac{7}{5}}}

= - \frac{4}{5 x ^{\frac{7}{5}}}

Popular Examples

integral of (-2)x

\int (- 2) x d x

integral from 0 to 1 of x^2sqrt(6x+8)

\int_{0}^{1} x^{2} 6 x + 8 d x

integral of ((7x^2+5x+7))/((x^2+1)^2)

\int \frac{( 7 x ^{2} + 5 x + 7 )}{( x ^{2} + 1 ) ^{2}} d x

derivative of (16/(x^2)-4/x)

\frac{d}{d x} (\frac{16}{x ^{2}} - \frac{4}{x})

derivative of f(x)=(a^{1/x}+b^{1/x})^x derivative of

f (x) = (a^{\frac{1}{x}} + b^{\frac{1}{x}})^{x}

Frequently Asked Questions (FAQ)

What is the derivative of 2/(\sqrt[5]{x^2}) ?
The derivative of 2/(\sqrt[5]{x^2}) is -4/(5x^{7/5)}
What is the first derivative of 2/(\sqrt[5]{x^2}) ?
The first derivative of 2/(\sqrt[5]{x^2}) is -4/(5x^{7/5)}