University:
Ohio State University
Course:
MATH 1151 | Calculus I
Academic year:

2021
Views:

367

Pages:

1
Author:

Leilani Contreras

REFERENCE PAGE 5 DIFFERENTIATION RULES GENERAL FORMULAS d/dx(c) = 0 d/dx[cf(x)] = cf'(x) d/dx[f(x)+g(x)] = f'(x)+g'(x) d/dx[f(x)-g(x)] = f'(x)-g'(x) d/dx[f(x)g(x)] = f(x)g'(x)+g(x)f'(x) (Product Rule) d/dx[f(x)/g(x)] = [g(x)f'(x)-f(x)g'(x)]/[g(x)]^2 (Quotient Rule) d/dx[f(g(x))] = f'(g(x))g'(x) (Chain Rule) d/dx(x^n) = nx^(n-1) (Power Rule) EXPONENTIAL AND LOGARITHMIC FUNCTIONS 9. d/dx(e^x) = e^x 10. d/dx(a^x) = a^x ln a 11. d/dx(ln|x|) = 1/x 12. d/dx(log_a x) = 1/(x ln a) TRIGONOMETRIC FUNCTIONS 13. d/dx(sin x) = cos x 14. d/dx(cos x) = -sin x 15. d/dx(tan x) = sec^2 x 16. d/dx(csc x) = -csc x cot x 17. d/dx(sec x) = sec x tan x 18. d/dx(cot x) = -csc^2 x INVERSE TRIGONOMETRIC FUNCTIONS 19. d/dx(sin^-1 x) = 1/sqrt(1-x^2) 20. d/dx(cos^-1 x) = -1/sqrt(1-x^2) 21. d/dx(tan^-1 x) = 1/(1+x^2) 22. d/dx(csc^-1 x) = -1/(|x|sqrt(x^2-1)) 23. d/dx(sec^-1 x) = 1/(|x|sqrt(x^2-1)) 24. d/dx(cot^-1 x) = -1/(1+x^2) HYPERBOLIC FUNCTIONS 25. d/dx(sinh x) = cosh x 26. d/dx(cosh x) = sinh x 27. d/dx(tanh x) = sech^2 x 28. d/dx(csch x) = -csch x coth x 29. d/dx(sech x) = -sech x tanh x 30. d/dx(coth x) = -csch^2 x INVERSE HYPERBOLIC FUNCTIONS 31. d/dx(sinh^-1 x) = 1/sqrt(1+x^2) 32. d/dx(cosh^-1 x) = 1/sqrt(x^2-1) 33. d/dx(tanh^-1 x) = 1/(1-x^2) 34. d/dx(csch^-1 x) = -1/(|x|sqrt(1+x^2)) 35. d/dx(sech^-1 x) = -1/(x sqrt(1-x^2)) 36. d/dx(coth^-1 x) = 1/(1-x^2)

Differentiation Rules Sheet

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