What is (\partial)/(\partial z)(zcos(xz)) ?

The answer to (\partial)/(\partial z)(zcos(xz)) is cos(zx)-zxsin(zx)

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(\partial)/(\partial z)(zcos(xz))

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

cos (z x) - z x sin (z x)

Solution steps

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

Treat

x

as a constant

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = z, g = cos (x z)

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

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

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

= 1 \cdot cos (x z) + (- sin (x z) x) z

Simplify

= cos (z x) - z x sin (z x)

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What is (\partial)/(\partial z)(zcos(xz)) ?
The answer to (\partial)/(\partial z)(zcos(xz)) is cos(zx)-zxsin(zx)