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

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

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

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

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

Solution steps

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

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

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

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

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