# How do you differentiate #g(x) =x^2cosx# using the product rule?

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To differentiate ( g(x) = x^2 \cos(x) ) using the product rule, let ( f(x) = x^2 ) and ( h(x) = \cos(x) ). Then, apply the product rule ( g'(x) = f'(x)h(x) + f(x)h'(x) ).

( f'(x) = 2x ) and ( h'(x) = -\sin(x) ).

So, ( g'(x) = (2x)(\cos(x)) + (x^2)(-\sin(x)) ).

( g'(x) = 2x \cos(x) - x^2 \sin(x) ).

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