What is (\partial)/(\partial y)(2xy^3+4) ?

The answer to (\partial)/(\partial y)(2xy^3+4) is 6xy^2

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(\partial)/(\partial y)(2xy^3+4)

\frac{\partial}{\partial y} (2 x y^{3} + 4)

6 x y^{2}

Solution steps

\frac{\partial}{\partial y} (2 x y^{3} + 4)

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} (4)

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

\frac{\partial}{\partial y} (4) = 0

= 6 x y^{2} + 0

Simplify

= 6 x y^{2}

\int 12 + 4 t^{2} d t

y^{^{''}} - 4 y^{^{'}} - 5 y = 0, y (1) = 0, y^{^{'}} (1) = 9

f (x) = 7 - 6 x, at x = 1

y^{2} \frac{d y}{d x} = y^{3} - x^{3}

x \to - 2 lim (x^{2} + 5)

What is (\partial)/(\partial y)(2xy^3+4) ?
The answer to (\partial)/(\partial y)(2xy^3+4) is 6xy^2