What is (\partial)/(\partial x)(3cos(x)-sin(xy)) ?

The answer to (\partial)/(\partial x)(3cos(x)-sin(xy)) is -3sin(x)-cos(xy)y

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(\partial)/(\partial x)(3cos(x)-sin(xy))

\frac{\partial}{\partial x} (3 cos (x) - sin (x y))

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

Solution steps

\frac{\partial}{\partial x} (3 cos (x) - sin (x y))

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (3 cos (x)) - \frac{\partial}{\partial x} (sin (x y))

\frac{\partial}{\partial x} (3 cos (x)) = - 3 sin (x)

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

= - 3 sin (x) - cos (x y) y

What is (\partial)/(\partial x)(3cos(x)-sin(xy)) ?
The answer to (\partial)/(\partial x)(3cos(x)-sin(xy)) is -3sin(x)-cos(xy)y