Most Important Selected Qs for JEE AdvancedMathematicsDifferentiation

If f(x)= _ n=1 ⁵⁰(x-n)^ n(51-n) ; then f(51) f^ (51)

Options

A4040
B1/1275
C1/4040
D1275

Correct answer

B. 1/1275

Step-by-step solution

aligned & f(x)= _ n=1 ⁵⁰(x-n)^ n(51-n) & (f(x))= _ n=1 ⁵⁰ n(51-n) (x-n) aligned Differentiating both side w.r.t. x aligned & f^ (x) f(x) = _ n=1 ⁵⁰ n(51-n) x-n & f^ (51) f(51) =1275 aligned

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