What is (\partial)/(\partial s)((z)(3r-s)) ?

The answer to (\partial)/(\partial s)((z)(3r-s)) is -z

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(\partial)/(\partial s)((z)(3r-s))

\frac{\partial}{\partial s} ((z) (3 r - s))

- z

Solution steps

\frac{\partial}{\partial s} ((z) (3 r - s))

Treat

z, r

as constants

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= z \frac{\partial}{\partial s} (3 r - s)

Apply the Sum/Difference Rule:

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

= z (\frac{\partial}{\partial s} (3 r) - \frac{\partial}{\partial s} (s))

\frac{\partial}{\partial s} (3 r) = 0

\frac{\partial}{\partial s} (s) = 1

= z (0 - 1)

Simplify

= - z

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What is (\partial)/(\partial s)((z)(3r-s)) ?
The answer to (\partial)/(\partial s)((z)(3r-s)) is -z