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

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

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

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

3 x^{2} y

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= 3 y x^{2} - 0

Simplify

= 3 x^{2} y

d (x) \frac{55}{0.01 x ^{2} + 1}

\int_{1}^{2} \frac{1}{x ^{6}} d x

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

\frac{d}{d x} ((6 x)^{- 5})

\frac{d}{d x} (x + \frac{3}{x})

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