Final Formula Sheet

The following formula will be made available while working the exam:
  1. ${d\over dx}[x^r] = rx^{r-1}$
  2. ${d\over dx}\big([g(x)]^r\big) = r[g(x)]^{r-1}g'(x)$
  3. ${d\over dx}\big[f(x)g(x)\big] = f'(x)g(x) + f(x)g'(x)$
  4. ${d\over dx}\left[{f(x)\over g(x)}\right] = {f'(x)g(x) - f(x)g'(x)\over\left[g(x)\right]^2}$
  5. ${d\over dx}f\big(g(x)\big)=f'\big(g(x)\big)g'(x)$
  6. ${d\over dx}e^{g(x)}=e^{g(x)}g'(x)$
  7. ${d\over dx}\ln g(x)={g'(x)\over g(x)}$
  8. $P(t)=P_0 e^{kt}$, $P(t)=P_0 e^{-\lambda t}$, $k,\lambda>0$
  9. $\int x^n={1\over n+1} x^{n+1}+C$, $n\ne -1$
  10. $\int {1\over x} dx = \ln |x| +C$
  11. $\int e^{ax} dx={1\over a}e^{ax}+C$, $a\ne 0$
  12. $\int \big[f(x)-g(x)\big]\,dx$