What is (\partial)/(\partial x)(x^3-5x^2y+7xy^3) ?

The answer to (\partial)/(\partial x)(x^3-5x^2y+7xy^3) is 3x^2-10yx+7y^3

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(\partial)/(\partial x)(x^3-5x^2y+7xy^3)

\frac{\partial}{\partial x} (x^{3} - 5 x^{2} y + 7 x y^{3})

3 x^{2} - 10 y x + 7 y^{3}

Solution steps

\frac{\partial}{\partial x} (x^{3} - 5 x^{2} y + 7 x y^{3})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x^{3}) - \frac{\partial}{\partial x} (5 x^{2} y) + \frac{\partial}{\partial x} (7 x y^{3})

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

\frac{\partial}{\partial x} (5 x^{2} y) = 10 y x

\frac{\partial}{\partial x} (7 x y^{3}) = 7 y^{3}

= 3 x^{2} - 10 y x + 7 y^{3}

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What is (\partial)/(\partial x)(x^3-5x^2y+7xy^3) ?
The answer to (\partial)/(\partial x)(x^3-5x^2y+7xy^3) is 3x^2-10yx+7y^3