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

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

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

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

3 y^{2}

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial y} (x^{2}) = 0

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

= 0 + 3 y^{2}

Simplify

= 3 y^{2}

\frac{d}{d x} (\frac{1 - 4 x}{5 + x})

\frac{d}{d x} (3 x^{2} - 4 x + 6)

y \to - 3 lim (y)

\int - e^{- 2 y} d y

\frac{d y}{d x} = 2 x - 3 y, y (0) = \frac{1}{3}

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