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

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

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

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

x y

Solution steps

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

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

\frac{\partial}{\partial z} (3 x y^{2}) = 0

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

= 0 - 0 + x y

Simplify

= x y

\int (x^{e} + 10 e^{x}) d x

t sin (5 t)

\int \frac{9 sin ( x )}{cos ^{3} ( x )} d x

x \to 1 lim (x^{\frac{2}{( 1 - x )}})

\int_{0}^{2} (x + 2) d x

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