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

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

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

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

3 z^{2}

Solution steps

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

Treat

x, y

as constants

Apply the Sum/Difference Rule:

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

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

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

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

= 3 z^{2} - 0

Simplify

= 3 z^{2}

y^{^{'}} = \frac{2 t}{y + t ^{2} y}

n \to \infty lim (\frac{1}{n !})

x \to 0 lim (\frac{1}{x ^{2} ( x + 8 )})

y^{^{''}} + 4 y = sin (2 x)

\int_{0}^{8} 3 x d x

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