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

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

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

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

3 y^{2}

Solution steps

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

Treat

z, x

as constants

Apply the Sum/Difference Rule:

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

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

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

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

= 0 + 3 y^{2}

Simplify

= 3 y^{2}

f (x) = x - 3 x^{\frac{1}{3}}

A n n - b

\int_{0}^{1} x^{2} cos (x^{3}) d x

\frac{d}{d x} (6 x^{7} - 2 x^{5} + 2)

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