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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

Respuesta :

Answer:

[tex]g'(x)=cos (x)-xsin(x)[/tex]

Step-by-step explanation:

If g(x)=x cos (x)

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

Using Product rule: [tex]{\left( {u\,v} \right)^\prime } = u'\,v + u\,v'[/tex]

[tex]u=x : u'=1\\v=cos (x): v'=-sin(x)[/tex]

Therefore:

[tex]g'(x)=cos (x)+x(-sin(x))\\g'(x)=cos (x)-xsin(x)[/tex]

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