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

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

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

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

- 2 y x

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (y^{3}) = 0

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

= 0 - 2 y x

Simplify

= - 2 y x

f (x) = 8 x^{9} - 3 x^{6} + 12 x^{3}

y = 4 x - x^{2}, y = 0

(X - 1) e^{X}

\frac{d y}{d x}, 4 y^{2} + 2 = 3 x^{2}

\int \frac{- 1}{x ^{2}} d x

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