What is (\partial)/(\partial y)(xy^3-x^2) ?

The answer to (\partial)/(\partial y)(xy^3-x^2) is 3xy^2

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(\partial)/(\partial y)(xy^3-x^2)

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

3 x y^{2}

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{\partial}{\partial y} (x^{2}) = 0

= 3 x y^{2} - 0

Simplify

= 3 x y^{2}

\frac{\partial}{\partial y} (x e^{- x^{2} y})

\int \frac{5 x ^{4}}{x ^{5} - 3} d x

n = 1 \sum \infty \frac{1}{2 n}

y = x^{2} - 4, y = - 2 x

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

What is (\partial)/(\partial y)(xy^3-x^2) ?
The answer to (\partial)/(\partial y)(xy^3-x^2) is 3xy^2