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Popular >

derivative of 1/(3\sqrt[3]{x^2})

Solution

Solution

- \frac{2}{9 x ^{\frac{5}{3}}}

Solution steps

Take the constant out:

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

Apply exponent rule:

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

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

Apply the chain rule:

- \frac{1}{3 ( x ^{2} ) ^{\frac{4}{3}}} \frac{d}{d x} (x^{2})

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

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

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

Simplify

\frac{1}{3} (- \frac{1}{3 ( x ^{2} ) ^{\frac{4}{3}}} \cdot 2 x) : - \frac{2}{9 x ^{\frac{5}{3}}}

= - \frac{2}{9 x ^{\frac{5}{3}}}

Popular Examples

integral from 1 to 4 of-9sqrt(x)ln(x)

\int_{1}^{4} - 9 x ln (x) d x

limit as x approaches 0 of (2e^{-x}-x^2+2x-2)/(4x^3)

x \to 0 lim (\frac{2 e ^{- x} - x ^{2} + 2 x - 2}{4 x ^{3}})

y^{^{'}} + x \cdot y = x \cdot y^{3}

sum from n=0 to infinity of 5(-4/3)^n

n = 0 \sum \infty 5 (- \frac{4}{3})^{n}

integral of (x^3-1/(x^2)-x^{2/3})

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

Frequently Asked Questions (FAQ)

What is the derivative of 1/(3\sqrt[3]{x^2}) ?
The derivative of 1/(3\sqrt[3]{x^2}) is -2/(9x^{5/3)}
What is the first derivative of 1/(3\sqrt[3]{x^2}) ?
The first derivative of 1/(3\sqrt[3]{x^2}) is -2/(9x^{5/3)}