What is (\partial)/(\partial y)(3y^2+10x^2y^2) ?

The answer to (\partial)/(\partial y)(3y^2+10x^2y^2) is 6y+20x^2y

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(\partial)/(\partial y)(3y^2+10x^2y^2)

\frac{\partial}{\partial y} (3 y^{2} + 10 x^{2} y^{2})

6 y + 20 x^{2} y

Solution steps

\frac{\partial}{\partial y} (3 y^{2} + 10 x^{2} y^{2})

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial y} (3 y^{2}) + \frac{\partial}{\partial y} (10 x^{2} y^{2})

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

\frac{\partial}{\partial y} (10 x^{2} y^{2}) = 20 x^{2} y

= 6 y + 20 x^{2} y

\frac{4}{1 + x ^{2}}

\frac{d}{d x} (\frac{1}{e})

\int \frac{1}{( e ^{2 x} + 4 )} d x

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

\int \frac{- x ^{2}}{2} d x

What is (\partial)/(\partial y)(3y^2+10x^2y^2) ?
The answer to (\partial)/(\partial y)(3y^2+10x^2y^2) is 6y+20x^2y