# given the graph of `f'(x)` and given that `g(x)=f(x)sinx` find `g''(0)`

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The function g(x) = f(x)*sin x.

g'(x) = f'(x)*sin x + f(x)*cos x

g''(x) = f''(x)*sin x + f'(x)*cos x + f'(x)*cos x - f(x)*sin x

g''(0) = f''(0)*sin 0 + f'(0)*cos 0 + f'(0)*cos 0 - f(0)*sin 0

= 0 + f'(0)*1 + f'(0)*1 - 0

From the graph of f'(x) that is given, f'(0) = 4

= 2*4

= 8

**The value of g''(0) = 8**