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If f(x)=(x-1)^(100)(x-2)^(2(99))(x-3)^(3(98))…(x-100)^(100), then the value of (f'(101))/(f(101)) is |
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Answer» 5050 TAKING log both sides, we get `log(f(x))=sum_(i=l)^(100)i(101-i)log(x-i)` Differentiating w.r.t. x, we get `(1)/(f(x)).f'(x)=sum_(i=l)^(100)(i(101-i))/((x-i))` `rArr""(f'(100))/(f(101))=sum_(i=l)^(100)((101-i)/(101-i))=5050` |
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