What is (\partial)/(\partial x)(z-sin(xy)) ?

The answer to (\partial)/(\partial x)(z-sin(xy)) is -ycos(xy)

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(\partial)/(\partial x)(z-sin(xy))

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

- y cos (x y)

Solution steps

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

Treat

z, y

as constants

Apply the Sum/Difference Rule:

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

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

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

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

= 0 - cos (x y) y

Simplify

= - y cos (x y)

What is (\partial)/(\partial x)(z-sin(xy)) ?
The answer to (\partial)/(\partial x)(z-sin(xy)) is -ycos(xy)