What is (\partial)/(\partial x)(y^2+6x-x^2y+36) ?

The answer to (\partial)/(\partial x)(y^2+6x-x^2y+36) is -2yx+6

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(\partial)/(\partial x)(y^2+6x-x^2y+36)

\frac{\partial}{\partial x} (y^{2} + 6 x - x^{2} y + 36)

- 2 y x + 6

Solution steps

\frac{\partial}{\partial x} (y^{2} + 6 x - x^{2} y + 36)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (y^{2}) + \frac{\partial}{\partial x} (6 x) - \frac{\partial}{\partial x} (x^{2} y) + \frac{\partial}{\partial x} (36)

\frac{\partial}{\partial x} (y^{2}) = 0

\frac{\partial}{\partial x} (6 x) = 6

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

\frac{\partial}{\partial x} (36) = 0

= 0 + 6 - 2 y x + 0

Simplify

= - 2 y x + 6

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What is (\partial)/(\partial x)(y^2+6x-x^2y+36) ?
The answer to (\partial)/(\partial x)(y^2+6x-x^2y+36) is -2yx+6