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

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

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

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

cos (x) - x sin (x)

Solution steps

\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)

= \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)

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

Simplify

= cos (x) - x sin (x)

\int - 4 x^{6} e^{x} d x

\int (2 + 5 x)^{2} d x

\int (x + 2) d x

3 x e^{- a x}

5 t^{2} y^{^{''}} + t y^{^{'}} - 12 y = 0

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