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

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

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

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

3 x z^{2} - 2 y

Solution steps

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

Treat

x, y

as constants

Apply the Sum/Difference Rule:

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

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

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

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

\frac{\partial}{\partial z} (2 yz) = 2 y

= 0 + 3 x z^{2} - 2 y

Simplify

= 3 x z^{2} - 2 y

\frac{d}{d x} (ln (\frac{3 x + 4}{3 x - 4}))

\int sin (t) 2 t d t

\int \frac{sin ( 2 x )}{e ^{x}} d x

l a pl a ce t r an s f or m 2 sin (2 t)

\frac{\partial}{\partial x} (7 e^{x} cos (yz))

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