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

The answer to (\partial)/(\partial y)(x^3y-3xy^2) is x^3-6xy

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

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

x^{3} - 6 x y

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial y} (3 x y^{2}) = 6 x y

= x^{3} - 6 x y

\int_{0}^{7} \frac{1}{49 + t ^{2}} d t

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

\frac{d}{d x} (4 + 1 - x)

\int_{0}^{1} 9 e^{x^{2}} d x

t^{2} y^{^{'}} + y^{^{'}} = t y

What is (\partial)/(\partial y)(x^3y-3xy^2) ?
The answer to (\partial)/(\partial y)(x^3y-3xy^2) is x^3-6xy