What is (\partial)/(\partial x)(x^6y-6x^2y^2) ?

The answer to (\partial)/(\partial x)(x^6y-6x^2y^2) is 6yx^5-12y^2x

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(\partial)/(\partial x)(x^6y-6x^2y^2)

\frac{\partial}{\partial x} (x^{6} y - 6 x^{2} y^{2})

6 y x^{5} - 12 y^{2} x

Solution steps

\frac{\partial}{\partial x} (x^{6} y - 6 x^{2} y^{2})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x^{6} y) - \frac{\partial}{\partial x} (6 x^{2} y^{2})

\frac{\partial}{\partial x} (x^{6} y) = 6 y x^{5}

\frac{\partial}{\partial x} (6 x^{2} y^{2}) = 12 y^{2} x

= 6 y x^{5} - 12 y^{2} x

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

What is (\partial)/(\partial x)(x^6y-6x^2y^2) ?
The answer to (\partial)/(\partial x)(x^6y-6x^2y^2) is 6yx^5-12y^2x