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

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

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

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

3 x^{2} y^{2}

Solution steps

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

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} (y)

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

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

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

Simplify

= 3 x^{2} y^{2}

f (x) = x^{2} - 4 x - 9

2 \frac{d ^{2} y}{d x ^{2}} - 6 \frac{d y}{d x} + 4 y = 2 sin (4 x)

\frac{\partial}{\partial x} (arctan (2 x + y))

y (1 + x^{2}) y^{^{'}} - x (4 + y^{2}) = 0

\int 9 sin^{3} (x) cos^{2} (x) d x

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