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

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

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

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

x^{2} - 3 x y^{2}

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= x^{2} - 3 x y^{2}

\frac{d y}{d x} = - 2 x y

\int x^{3} e x^{4} + 5 d x

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

\frac{\partial}{\partial t} (e^{π t})

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

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