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

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

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

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

6 x y^{2}

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= 6 x y^{2} + 0

Simplify

= 6 x y^{2}

\frac{4}{x + 2}

\int \frac{4 t ^{3} - 3 t ^{2} + 4 t}{t ^{2} + 1} d t

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

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

\int_{0}^{1} \frac{49}{x ^{5}} d x

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