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Popular >

derivative of 1/(x^{2/3})

Solution

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

Solution

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

Solution steps

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

Apply exponent rule:

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

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

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= - \frac{2}{3} x^{- \frac{2}{3} - 1}

Simplify

- \frac{2}{3} x^{- \frac{2}{3} - 1} : - \frac{2}{3 x ^{\frac{5}{3}}}

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

Popular Examples

limit as x approaches 1 of arcsin(x)

x \to 1 lim (arcsin (x))

derivative of (4x^2-5x+1/(3x+7))

\frac{d}{d x} (\frac{4 x ^{2} - 5 x + 1}{3 x + 7})

integral from 1 to 4 of (5x^2+sqrt(x))

\int_{1}^{4} (5 x^{2} + x) d x

csc(y)+sec^2(x)((dy)/(dx))=0

csc (y) + sec^{2} (x) (\frac{d y}{d x}) = 0

sum from n=1 to infinity of 3/(n(n+1))

n = 1 \sum \infty \frac{3}{n ( n + 1 )}

Frequently Asked Questions (FAQ)

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