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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) $f(x)=1 / x$

(a) $f^{(n)}(x)=n !$(b) $f^{(n)}(x)=(-1)^{n} \frac{n !}{x^{n+1}}$

Calculus 1 / AB

Chapter 3

Derivatives

Section 3

Basic Differentiation Formulas

Campbell University

Idaho State University

Boston College

Lectures

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Hi, this is Claire. So instruction 3.3. Number 50. Ito's too. It's about calculus book. You're gonna find the interpretive of each function with party we're going to for the first few d'oeuvres it it's so the first derivative moves in Times X on Linus Ling. This is just a power formula. So if you do this with a second or a bit of then time, Linus long next ones, too. They're driven sometimes a new awareness planning. I still x to the n minus three. And here we have a clear, um you pattern So are conservative equal to n factorial. Moving on to part B. We're going to do the same. The same approach. You could have one over X square, second derivative wounds. I could have one square two over x cute. In our third derivative, I get a one you mystery over next to the flaws. And here we have another pattern. Sonar, and they're a bit of ends. They could have one to the end Pictorial over. Next on dde waas One books for answer and we're done

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