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

3 Answers

  • 1 decade ago
    Favorite 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 4
    4 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

  • Anonymous
    1 decade ago

    the nth derivative of x^n = n!

    the nth derivative of 1/x = (-1)^n n! / x^(n+1)

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