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

The answer to (\partial)/(\partial x)(sin(x)-cos(xy)) is cos(x)+ysin(xy)

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

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

cos (x) + y sin (x y)

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= cos (x) - (- sin (x y) y)

Simplify

= cos (x) + y sin (x y)

What is (\partial)/(\partial x)(sin(x)-cos(xy)) ?
The answer to (\partial)/(\partial x)(sin(x)-cos(xy)) is cos(x)+ysin(xy)