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

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

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(\partial)/(\partial y)(xy+z^3)

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

x

Solution steps

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

Treat

x, z

as constants

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial y} (x y) = x

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

= x + 0

Simplify

= x

\int \frac{1}{e ^{\frac{x}{2}} + e ^{x}} d x

\frac{d}{d x} (sin (ln (x^{2})))

\int x^{2} e^{a x} d x

y^{^{'}} = y tan (x) + sin (x)

\int - x + 8 d x

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