What is (\partial)/(\partial z)(x^4y+xz-yz^2-7) ?

The answer to (\partial)/(\partial z)(x^4y+xz-yz^2-7) is x-2yz

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(\partial)/(\partial z)(x^4y+xz-yz^2-7)

\frac{\partial}{\partial z} (x^{4} y + x z - y z^{2} - 7)

x - 2 yz

Solution steps

\frac{\partial}{\partial z} (x^{4} y + x z - y z^{2} - 7)

Treat

x, y

as constants

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial z} (x^{4} y) + \frac{\partial}{\partial z} (x z) - \frac{\partial}{\partial z} (y z^{2}) - \frac{\partial}{\partial z} (7)

\frac{\partial}{\partial z} (x^{4} y) = 0

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

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

\frac{\partial}{\partial z} (7) = 0

= 0 + x - 2 yz - 0

Simplify

= x - 2 yz

\int x^{y} d x

\frac{d}{d x} (cos (x) - x \cdot sin (x))

\frac{1}{s + a}

x^{3} - 3 x^{2} + x - 5

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

What is (\partial)/(\partial z)(x^4y+xz-yz^2-7) ?
The answer to (\partial)/(\partial z)(x^4y+xz-yz^2-7) is x-2yz