How do I solve this equation?

Question

If $f(x)=(x-1)^2 sinx$ , then $f'(0)=?$

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Answer 1 · 2018-04-15T19:18:37

$f'(0)=1$

we have to use the product rule

$f(x)=color(red)(u)v=>f'(x)=color(red)(u')v+color(red)(u)v'$

$f(x)=(x-1)^2sinx$

$color(red)(u=(x-1)^2=>u'=2(x-1))$

$v=sinx=>v'=cosx$

$:.f'(x)=color(red)(2(x-1))sinx+color(red)((x-1)^2)cosx$

$:. f'(0)=cancel(2(0-1)sin0)+(0-1)^2cos0$

$f'(0)=1xx1=1$