What is (\partial)/(\partial z)(5x^2-3xy+xyz) ?

The answer to (\partial)/(\partial z)(5x^2-3xy+xyz) is xy

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(\partial)/(\partial z)(5x^2-3xy+xyz)

\frac{\partial}{\partial z} (5 x^{2} - 3 x y + x yz)

x y

Solution steps

\frac{\partial}{\partial z} (5 x^{2} - 3 x y + x yz)

Treat

x, y

as constants

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial z} (5 x^{2}) - \frac{\partial}{\partial z} (3 x y) + \frac{\partial}{\partial z} (x yz)

\frac{\partial}{\partial z} (5 x^{2}) = 0

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

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

= 0 - 0 + x y

Simplify

= x y

\frac{\partial}{\partial t} (ln (3 x + 3 c t))

x \to 0 lim (\frac{1}{x} - \frac{1}{e ^{x}})

\frac{1}{( s ^{2} + 1 ) ( s ^{2} + 16 )}

x \to 2 lim (x^{2} - 4 x + 5)

\frac{d}{d x} (- \frac{2 x}{( x ^{2} - 1 ) ^{2}})

What is (\partial)/(\partial z)(5x^2-3xy+xyz) ?
The answer to (\partial)/(\partial z)(5x^2-3xy+xyz) is xy