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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{x}{2}) = \frac{1}{2}

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

Simplify

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

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

Popular Examples

derivative of xy^2-x^3y

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

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

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

(\partial)/(\partial x)(cos(3x+yz)*3)

\frac{\partial}{\partial x} (cos (3 x + yz) \cdot 3)

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

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

integral from 0 to 3 of sin^2(mx)

\int_{0}^{3} sin^{2} (m x) d x

Frequently Asked Questions (FAQ)

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