What is (\partial)/(\partial x)(\sqrt[3]{xy}) ?

The answer to (\partial)/(\partial x)(\sqrt[3]{xy}) is (y^{1/3})/(3x^{2/3)}

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(\partial)/(\partial x)(\sqrt[3]{xy})

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

Solution steps

Treat

y

as a constant

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (x y) = y

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

Simplify

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

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

\int u^{\frac{1}{2}} d u

f (x) = 7 x^{3} x

f (x) = \frac{x - 1}{x - 2}, at x = 3

\int \frac{( sin ( 2 x ) )}{cos ( x )} d x

y^{^{'}} + 2 y = 18

What is (\partial)/(\partial x)(\sqrt[3]{xy}) ?
The answer to (\partial)/(\partial x)(\sqrt[3]{xy}) is (y^{1/3})/(3x^{2/3)}