Find the nth derivative of each function by calculating the first few derivatives?
and observing the pattern that occurs.
a) f (x) = x^n
b) f (x) = 1/x
- 1 decade agoFavorite Answer
x^1 = 1, x^2 = 2x, x^3 = 3x^2
Bring the power down to the coefficient and the power of x is n-1. This is the power rule.
1/x is x^-1 so do the same thing.
- ?Lv 44 years ago
basically keep taking derivatives of your derivatives till you attain the nth derviative. in case you have a ordinary algebraic function (study polynomial), at last you will get 0 as your answer. if the degree of your polymonial is okay, then the ok-th derivative would be a continuing (that's nicely ok!) and the (ok+a million)-st derivative would be 0
- Anonymous1 decade ago
the nth derivative of x^n = n!
the nth derivative of 1/x = (-1)^n n! / x^(n+1)