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

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

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(\partial)/(\partial x)(xcos(xy))

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

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

Solution steps

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

Treat

y

as a constant

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

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

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

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

Simplify

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

f (x) = x^{3} + 1

\frac{d}{d x} (arctan (x^{4} y^{3}))

\int \frac{x + 3}{x + 6} d x

x \to 0 + lim (\frac{2}{1 + ln ( x )})

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