n^ th derivative of x^ n + 1 is - Vidyadip

MCQ

${n^{th}}$ derivative of ${x^{n + 1}}$ is

✓
$(n + 1)!x$
B
$(n + 1)!$
C
$n!x$
D
$n!$

✓

Answer

Correct option: A.

$(n + 1)!x$

a
(a) Let $y = {x^{n + 1}};$ then ${y_1} = (n + 1){x^n}$

${y_2} = n(n + 1){x^{n - 1}}$

${y_3} = n(n + 1)(n - 1){x^{n - 2}}$
.....................................
...................................
${y_n} = (n + 1)!x$.

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