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

The answer to (\partial)/(\partial y)(3y^2x+x^3+yx^2) is x^2+6yx

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

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

x^{2} + 6 y x

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial y} (3 y^{2} x) = 6 x y

\frac{\partial}{\partial y} (x^{3}) = 0

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

= 6 x y + 0 + x^{2}

Simplify

= x^{2} + 6 y x

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What is (\partial)/(\partial y)(3y^2x+x^3+yx^2) ?
The answer to (\partial)/(\partial y)(3y^2x+x^3+yx^2) is x^2+6yx