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Popular >

derivative of \sqrt[3]{xy}

Solution

Solution

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

Solution steps

Apply the chain rule:

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

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

\frac{d}{d x} (x y) = y + x \frac{d y}{d x}

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

Simplify

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

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

Popular Examples

integral of (8x^5-5x^4-4x^3-6x^2-2x-3)

\int (8 x^{5} - 5 x^{4} - 4 x^{3} - 6 x^{2} - 2 x - 3) d x

derivative of (30000)/(1.8t+9)derivative of

\frac{30000}{1.8 t + 9}

integral of 1/(4-3x)

\int \frac{1}{4 - 3 x} d x

slope of (2.5)(-1.7)slope

(2.5) (- 1.7)

limit as x approaches 0 of (x^4)/(x^2)

x \to 0 lim (\frac{x ^{4}}{x ^{2}})

Frequently Asked Questions (FAQ)

What is the derivative of \sqrt[3]{xy} ?
The derivative of \sqrt[3]{xy} is (y+x\frac{dy)/(dx)}{3(xy)^{2/3}}
What is the first derivative of \sqrt[3]{xy} ?
The first derivative of \sqrt[3]{xy} is (y+x\frac{dy)/(dx)}{3(xy)^{2/3}}