What is (\partial)/(\partial x)(3xy^2-2y+5x^2y^2) ?

The answer to (\partial)/(\partial x)(3xy^2-2y+5x^2y^2) is 3y^2+10xy^2

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(\partial)/(\partial x)(3xy^2-2y+5x^2y^2)

\frac{\partial}{\partial x} (3 x y^{2} - 2 y + 5 x^{2} y^{2})

3 y^{2} + 10 x y^{2}

Solution steps

\frac{\partial}{\partial x} (3 x y^{2} - 2 y + 5 x^{2} y^{2})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (3 x y^{2}) - \frac{\partial}{\partial x} (2 y) + \frac{\partial}{\partial x} (5 x^{2} y^{2})

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

\frac{\partial}{\partial x} (2 y) = 0

\frac{\partial}{\partial x} (5 x^{2} y^{2}) = 10 y^{2} x

= 3 y^{2} - 0 + 10 y^{2} x

Simplify

= 3 y^{2} + 10 x y^{2}

What is (\partial)/(\partial x)(3xy^2-2y+5x^2y^2) ?
The answer to (\partial)/(\partial x)(3xy^2-2y+5x^2y^2) is 3y^2+10xy^2