What is (\partial)/(\partial x)(xcos(x)y) ?

The answer to (\partial)/(\partial x)(xcos(x)y) is y(cos(x)-xsin(x))

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(\partial)/(\partial x)(xcos(x)y)

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

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

f = x, g = cos (x)

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

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

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

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

Simplify

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

What is (\partial)/(\partial x)(xcos(x)y) ?
The answer to (\partial)/(\partial x)(xcos(x)y) is y(cos(x)-xsin(x))