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To differentiate, we need to use the chain rule.
Let sinx = u ==> u' = cosx
==> We know that: (u^5)' = 5*u'*u^4
==> Now we will substitute:
==> (sin^5 x)' = 5*cosx* sin^4 x
Then , the derivative of sin^5 x is 5cosx*sin^4 x
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