A) \[(n+1)!x\]
B) \[(n+1)!\]
C) \[n!x\]
D) \[n!\]
Correct Answer: A
Solution :
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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