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

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

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

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

3 x^{2} y^{2} + 3 y - 8 x y

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

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

= 3 y^{2} x^{2} - 8 y x + 3 y - 0

Simplify

= 3 x^{2} y^{2} + 3 y - 8 x y

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