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STD 12 - 5. continuity and differentiation — Mathematics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceMathematicsSTD 12 - 5. continuity and differentiation1 Mark
MCQ
The nth derivative of $x{e^x}$ vanishes when
  • A
    $x = 0$
  • B
    $x = - 1$
  • ✓
    $x = - n$
  • D
    $x = n$
✓

Answer

Correct option: C.
$x = - n$
c
(c) $f(x) = x{e^x}$
$f'(x) = {e^x} + x{e^x}$
$f''(x) = {e^x} + {e^x} + x{e^x} = 2{e^x} + x{e^x}$
$f'''(x) = 2{e^x} + {e^x} + x{e^x} = 3{e^x} + x{e^x}$
……………………………………………
……………………………………………
${f^n}(x) = n{e^x} + x{e^x}$. 

Now, ${f^n}(x) = 0$

==> $n{e^x} + x{e^x} = 0$ ==>$x = - n$.

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