1. ## calculus stupidity....

I'm reading a problem in my book and they are going over the solution to a problem: If f(x) = 1/x, then f^4 (x) = 24/x^5.... How the heck did they get that? If I take the function to the 4th power, I get 1/(x^4)... Am I not mistaken?

2. If written as $\displaystyle f^{(4)}(x)$, then it means the derivative of the 4th order (the parentheses are important).

3. thats the 4th derivative of the function

f(x)=1/x

$\displaystyle \frac{df(x)}{dx}= \frac{-1}{x^2}$

$\displaystyle \frac{d^2f(x)}{dx^2}= \frac{2}{x^3}$

$\displaystyle \frac{d^3f(x)}{dx^3}= \frac{-6}{x^4}$

$\displaystyle \frac{d^4f(x)}{dx^4}= \frac{24}{x^5}$

4. Ah, that would explain it, never seen it written that way, i always assumed f''''(x). Thanks.

5. More generally, if $\displaystyle \displaystyle f(x) = \frac{1}{x}$, then:

$\displaystyle \displaystyle f^n(x) = \frac{(-1)^n\prod_{k=0}^{n-1}\left(n-k\right)}{x^{n+1}}$.

6. Originally Posted by bobbooey
Ah, that would explain it, never seen it written that way, i always assumed f''''(x). Thanks.
So what do you assume for the 37th derivative?