What is (\partial)/(\partial z)(5xsin(y-z)) ?

The answer to (\partial)/(\partial z)(5xsin(y-z)) is -5xcos(y-z)

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(\partial)/(\partial z)(5xsin(y-z))

\frac{\partial}{\partial z} (5 x sin (y - z))

- 5 x cos (y - z)

Solution steps

\frac{\partial}{\partial z} (5 x sin (y - z))

Treat

x, y

as constants

Take the constant out:

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

= 5 x \frac{\partial}{\partial z} (sin (y - z))

Apply the chain rule:

cos (y - z) \frac{\partial}{\partial z} (y - z)

= cos (y - z) \frac{\partial}{\partial z} (y - z)

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

= 5 x cos (y - z) (- 1)

Simplify

= - 5 x cos (y - z)

What is (\partial)/(\partial z)(5xsin(y-z)) ?
The answer to (\partial)/(\partial z)(5xsin(y-z)) is -5xcos(y-z)