1. Let f(x) = 1/(1+x) for x ¹ -1. What is the nth derivative, f(n)(x)?
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A. n!(1+x)n+1 |
B. –n!/(1+x)n+1 |
C. n!/(1+x)n+1 |
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D. –n!/(1+x)n |
E. (-1)nn!/(1+x)n+1 |
Solution: The answer is E
To find the nth derivative of f(x), take a few consecutive derivatives starting with the first and try to recognize a pattern as follows,
