What is (\partial)/(\partial y)(x^4y^2-x^3y) ?

The answer to (\partial)/(\partial y)(x^4y^2-x^3y) is 2x^4y-x^3

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(\partial)/(\partial y)(x^4y^2-x^3y)

\frac{\partial}{\partial y} (x^{4} y^{2} - x^{3} y)

2 x^{4} y - x^{3}

Solution steps

\frac{\partial}{\partial y} (x^{4} y^{2} - x^{3} y)

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial y} (x^{4} y^{2}) - \frac{\partial}{\partial y} (x^{3} y)

\frac{\partial}{\partial y} (x^{4} y^{2}) = 2 x^{4} y

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

= 2 x^{4} y - x^{3}

\frac{d}{d x} (2 x^{3} + 1)

f (x) = \frac{e ^{x}}{4 - 4 x}

\frac{\partial}{\partial y} (sin^{2} (x + y))

f (x) = 6 - x^{2}, g (x) = x

1 - 3 x

What is (\partial)/(\partial y)(x^4y^2-x^3y) ?
The answer to (\partial)/(\partial y)(x^4y^2-x^3y) is 2x^4y-x^3