What is (\partial)/(\partial x)(cos(xz)+sin(yz)-z) ?

The answer to (\partial)/(\partial x)(cos(xz)+sin(yz)-z) is -zsin(xz)

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(\partial)/(\partial x)(cos(xz)+sin(yz)-z)

\frac{\partial}{\partial x} (cos (x z) + sin (yz) - z)

- z sin (x z)

Solution steps

\frac{\partial}{\partial x} (cos (x z) + sin (yz) - z)

Treat

z, y

as constants

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (cos (x z)) + \frac{\partial}{\partial x} (sin (yz)) - \frac{\partial}{\partial x} (z)

\frac{\partial}{\partial x} (cos (x z)) = - sin (x z) z

\frac{\partial}{\partial x} (sin (yz)) = 0

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

= - sin (x z) z + 0 - 0

Simplify

= - z sin (x z)

What is (\partial)/(\partial x)(cos(xz)+sin(yz)-z) ?
The answer to (\partial)/(\partial x)(cos(xz)+sin(yz)-z) is -zsin(xz)