What is (\partial)/(\partial x)(x^{1/3}y^3) ?

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

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(\partial)/(\partial x)(x^{1/3}y^3)

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

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

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

\int \frac{5 x - 4}{2 x ^{2} + x - 1} d x

t \to 0 lim (\frac{sin ( 4 t )}{t})

65 x^{\frac{9}{10}}

y^{^{'}} + 2 y = 5 sin (e^{2 x})

\int x cos (\frac{x}{3}) d x

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