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

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

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

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

2 z x

Solution steps

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

Treat

x, y

as constants

Apply the Sum/Difference Rule:

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

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

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

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

= 2 x z + 0

Simplify

= 2 z x

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

\int \frac{1}{5 - 4 x ^{2}} d x

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