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

The answer to (\partial)/(\partial y)(y^3+xy^2+y) is 3y^2+2xy+1

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(\partial)/(\partial y)(y^3+xy^2+y)

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

3 y^{2} + 2 x y + 1

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

\frac{\partial}{\partial y} (y) = 1

= 3 y^{2} + 2 x y + 1

\int \frac{x ^{2}}{x ^{6} + 9} d x

\frac{\partial}{\partial x} (lo g_{e} (x^{2} + y^{2}))

y = x^{2}, y = 2 x

\frac{d}{d x} (x^{2} ln (2 x + 1))

\int x^{13} e^{x^{14}} d x

What is (\partial)/(\partial y)(y^3+xy^2+y) ?
The answer to (\partial)/(\partial y)(y^3+xy^2+y) is 3y^2+2xy+1