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

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

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(\partial)/(\partial x)(x^4-x^3y+xy^3-y^4)

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

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

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

\frac{\partial}{\partial x} (y^{4}) = 0

= 4 x^{3} - 3 y x^{2} + y^{3} - 0

Simplify

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

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