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

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

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

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

3 y^{2} x^{2} - 4 y x + 3

Solution steps

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

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

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

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

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

= 3 y^{2} x^{2} - 4 y x + 3

\frac{d}{d x} (3 sin (2))

g (x) = \frac{1}{5 x ^{2} + 2 x}

y^{^{''}} + 5 y^{^{'}} + 6.25 y = 0

\frac{d}{d x} (5 x - 2 x^{2})

\int_{1}^{4} x^{\frac{1}{2}} ln (x) d x

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