What is (\partial)/(\partial x)(z*cos(y*x)) ?

The answer to (\partial)/(\partial x)(z*cos(y*x)) is -zysin(yx)

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(\partial)/(\partial x)(zcos(yx))

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

- zy sin (y x)

Solution steps

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

Treat

z, y

as constants

Take the constant out:

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

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

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (y x) = y

= z (- sin (y x) y)

Simplify

= - zy sin (y x)

What is (\partial)/(\partial x)(z*cos(y*x)) ?
The answer to (\partial)/(\partial x)(z*cos(y*x)) is -zysin(yx)