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

The answer to (\partial)/(\partial x)(3-3x+4y-4x^2y) is -8xy-3

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(\partial)/(\partial x)(3-3x+4y-4x^2y)

\frac{\partial}{\partial x} (3 - 3 x + 4 y - 4 x^{2} y)

- 8 x y - 3

Solution steps

\frac{\partial}{\partial x} (3 - 3 x + 4 y - 4 x^{2} y)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (3) - \frac{\partial}{\partial x} (3 x) + \frac{\partial}{\partial x} (4 y) - \frac{\partial}{\partial x} (4 x^{2} y)

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

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

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

\frac{\partial}{\partial x} (4 x^{2} y) = 8 y x

= 0 - 3 + 0 - 8 y x

Simplify

= - 8 x y - 3

What is (\partial)/(\partial x)(3-3x+4y-4x^2y) ?
The answer to (\partial)/(\partial x)(3-3x+4y-4x^2y) is -8xy-3