What is (\partial)/(\partial z)(x^2y-3xz+5y+7z) ?

The answer to (\partial)/(\partial z)(x^2y-3xz+5y+7z) is -3x+7

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(\partial)/(\partial z)(x^2y-3xz+5y+7z)

\frac{\partial}{\partial z} (x^{2} y - 3 x z + 5 y + 7 z)

- 3 x + 7

Solution steps

\frac{\partial}{\partial z} (x^{2} y - 3 x z + 5 y + 7 z)

Treat

x, y

as constants

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial z} (x^{2} y) - \frac{\partial}{\partial z} (3 x z) + \frac{\partial}{\partial z} (5 y) + \frac{\partial}{\partial z} (7 z)

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

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

\frac{\partial}{\partial z} (5 y) = 0

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

= 0 - 3 x + 0 + 7

Simplify

= - 3 x + 7

\frac{d}{d x} (20 sin (x))

\int - \frac{10}{x ^{11}} d x

\frac{\partial}{\partial x} (\frac{y + x}{y + z})

\frac{\partial}{\partial x} (ln (x) - 2)

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

What is (\partial)/(\partial z)(x^2y-3xz+5y+7z) ?
The answer to (\partial)/(\partial z)(x^2y-3xz+5y+7z) is -3x+7