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

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

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

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

3 y - 3 x^{2}

Solution steps

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

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

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

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

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

= 0 + 3 y - 3 x^{2}

Simplify

= 3 y - 3 x^{2}

e^{- x^{3}}

\int \frac{x}{u}

\int y - x

y = x^{3}, 0 \leq x \leq 3

\int (10 x - 7) d x

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