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Calculus Volume 2

B | Table of Derivatives

Calculus Volume 2B | 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)=nxn1,for real numbersnddx(xn)=nxn1,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)=11x2ddx(sin−1x)=11x2

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

17. ddx(sec−1x)=1|x|x21ddx(sec−1x)=1|x|x21

18. ddx(cos−1x)=11x2ddx(cos−1x)=11x2

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

20. ddx(csc−1x)=1|x|x21ddx(csc−1x)=1|x|x21

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)=11x2(|x|<1)ddx(tanh−1x)=11x2(|x|<1)

33. ddx(sech−1x)=1x1x2(0<x<1)ddx(sech−1x)=1x1x2(0<x<1)

34. ddx(cosh−1x)=1x21(x>1)ddx(cosh−1x)=1x21(x>1)

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

36. ddx(csch−1x)=1|x|1+x2(x0)ddx(csch−1x)=1|x|1+x2(x0)

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