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Differentiation question

2003 · Shift 0 · Q116

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PYQ Library
JEE Main
Mathematics
Differentiation
2003 · Shift 0 · Q116

Differentiation question

2003 · Shift 0 · Q116

JEE MainMathematicsDifferentiationMCQ+4 / −1

If

f\left( x \right) = {x^n},

then the value of

f\left( 1 \right) - {{f'\left( 1 \right)} \over {1!}} + {{f''\left( 1 \right)} \over {2!}} - {{f'''\left( 1 \right)} \over {3!}} + ..........{{{{\left( { - 1} \right)}^n}{f^n}\left( 1 \right)} \over {n!}}

is

A
$1$
B
${{2^n}}$
C
${{2^n} - 1}$
D
$0$

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