Question

Let g ( x ) = x cos ⁡ ( x ) g(x)=xcos(x)g, left parenthesis, x, right parenthesis, equals, x, cosine, left parenthesis, x, right parenthesis. Find g ′ ( x ) g ′ (x)g, prime, left parenthesis, x, right parenthesis

Answer 1

`g'(x)=cos (x)-xsin(x)`

Explanation:

If g(x)=x cos (x)

We want to determine the derivative of g(x).

Using Product rule:
`{\left( {u\,v} \right)^\prime } = u'\,v + u\,v'`

`u=x : u'=1\\v=cos (x): v'=-sin(x)`

Therefore:

`g'(x)=cos (x)+x(-sin(x))\\g'(x)=cos (x)-xsin(x)`