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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

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

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

\frac{d y}{d x} = y^{2} e^{- 2 x}

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

e^{m x}

y = 9 - 0.25 x^{2}, y = 1, 2 < x < 5

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