Calculus Volume 3

# B | Table of Derivatives

Calculus Volume 3B | Table of Derivatives

## General Formulas

1. $ddx(c)=0ddx(c)=0$

2. $ddx(f(x)+g(x))=f′(x)+g′(x)ddx(f(x)+g(x))=f′(x)+g′(x)$

3. $ddx(f(x)g(x))=f′(x)g(x)+f(x)g′(x)ddx(f(x)g(x))=f′(x)g(x)+f(x)g′(x)$

4. $ddx(xn)=nxn−1,for real numbersnddx(xn)=nxn−1,for real numbersn$

5. $ddx(cf(x))=cf′(x)ddx(cf(x))=cf′(x)$

6. $ddx(f(x)−g(x))=f′(x)−g′(x)ddx(f(x)−g(x))=f′(x)−g′(x)$

7. $ddx(f(x)g(x))=g(x)f′(x)−f(x)g′(x)(g(x))2ddx(f(x)g(x))=g(x)f′(x)−f(x)g′(x)(g(x))2$

8. $ddx[f(g(x))]=f′(g(x))·g′(x)ddx[f(g(x))]=f′(g(x))·g′(x)$

## Trigonometric Functions

9. $ddx(sinx)=cosxddx(sinx)=cosx$

10. $ddx(tanx)=sec2xddx(tanx)=sec2x$

11. $ddx(secx)=secxtanxddx(secx)=secxtanx$

12. $ddx(cosx)=−sinxddx(cosx)=−sinx$

13. $ddx(cotx)=−csc2xddx(cotx)=−csc2x$

14. $ddx(cscx)=−cscxcotxddx(cscx)=−cscxcotx$

## Inverse Trigonometric Functions

15. $ddx(sin−1x)=11−x2ddx(sin−1x)=11−x2$

16. $ddx(tan−1x)=11+x2ddx(tan−1x)=11+x2$

17. $ddx(sec−1x)=1|x|x2−1ddx(sec−1x)=1|x|x2−1$

18. $ddx(cos−1x)=−11−x2ddx(cos−1x)=−11−x2$

19. $ddx(cot−1x)=−11+x2ddx(cot−1x)=−11+x2$

20. $ddx(csc−1x)=−1|x|x2−1ddx(csc−1x)=−1|x|x2−1$

## Exponential and Logarithmic Functions

21. $ddx(ex)=exddx(ex)=ex$

22. $ddx(ln|x|)=1xddx(ln|x|)=1x$

23. $ddx(bx)=bxlnbddx(bx)=bxlnb$

24. $ddx(logbx)=1xlnbddx(logbx)=1xlnb$

## Hyperbolic Functions

25. $ddx(sinhx)=coshxddx(sinhx)=coshx$

26. $ddx(tanhx)=sech2xddx(tanhx)=sech2x$

27. $ddx(sechx)=−sechxtanhxddx(sechx)=−sechxtanhx$

28. $ddx(coshx)=sinhxddx(coshx)=sinhx$

29. $ddx(cothx)=−csch2xddx(cothx)=−csch2x$

30. $ddx(cschx)=−cschxcothxddx(cschx)=−cschxcothx$

## Inverse Hyperbolic Functions

31. $ddx(sinh−1x)=1x2+1ddx(sinh−1x)=1x2+1$

32. $ddx(tanh−1x)=11−x2(|x|<1)ddx(tanh−1x)=11−x2(|x|<1)$

33. $ddx(sech−1x)=−1x1−x2(0

34. $ddx(cosh−1x)=1x2−1(x>1)ddx(cosh−1x)=1x2−1(x>1)$

35. $ddx(coth−1x)=11−x2(|x|>1)ddx(coth−1x)=11−x2(|x|>1)$

36. $ddx(csch−1x)=−1|x|1+x2(x≠0)ddx(csch−1x)=−1|x|1+x2(x≠0)$

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