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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = cos (x y), g = x

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

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

\frac{\partial}{\partial x} (x) = 1

= (- sin (x y) y) x + 1 \cdot cos (x y)

Simplify

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

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