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

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

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

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

3 y^{2}

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= 0 + 3 y^{2}

Simplify

= 3 y^{2}

\int 3 x sin (x^{2}) d x

y^{^{'''}} + 6 y^{^{''}} + 9 y^{^{'}} = 0

\int_{1}^{6} \frac{2}{x - 11} d x

\frac{d x}{d t} + 4 \cdot 1 0^{- 4} x = 8 \cdot 1 0^{- 5}, x (0) = 1

f (x) = 3 x^{2} - 5 x + 1

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