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JEE MATHEMATICS MCQ: DIFFERENTIATION

1 Easy
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Analyzing +4 | -1
If f(x)=(1−x)nf\left( x \right) = {\left( {1 - x} \right)^n}, then the value of f(0)+f′(0)+f′′(0)2!+…fn(0)n!f\left( 0 \right) + f'\left( 0 \right) + \frac{{f''\left( 0 \right)}}{{2!}} + \ldots \frac{{{f^n}\left( 0 \right)}}{{n!}}, is
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Correct option: B
0
Option B (0) is correct because the given expression is the binomial expansion of (1−1)n(1-1)^n, which equals 0.

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