DifferentiationIntegrationRules

DifferentiationIntegrationRules - Differentiation Rules...

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Unformatted text preview: Differentiation Rules Calculus I General Formulas 1. 2. 3. 4. 5. d dx k Integration Formulas Calculus I General Formulas 1. k dx = kx + C. (u + v) dx = (u - v) dx = u dv = uv - u dx + u dx - v dx. v dx. = 0. + v) = - v) = du dx du dx d dx (u d dx (u + - dv dx . dv dx v. 2. 3. 4. d dx (uv) d u dx ( v ) dv = u dx + v du . dx dv v du -u dx dx v2 v du. (Integration by parts) = . dy dx 5. No "Quotient Rule". = dy du du dx . 6. y = f (u), u = u(x), Basic Functions 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. d n dx u d dx 6. f (u) du = f (u(x))u (x) dx. (Substitution) Basic Formulas 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. un du = 1 u 1 n+1 n+1 u = nun-1 du . dx 1 du u dx . + C; n = -1. ln |u| = du = ln |u| + C. d u dx e d dx d dx d dx d dx d dx d dx d dx d dx d dx d dx d dx d dx d dx d dx d dx d dx = eu du . dx eu du = eu + C. sin u du = - cos u + C. cos u du = sin u + C. sec2 u du = tan u + C. sec u tan u du = sec u + C. csc2 u du = - cot u + C. csc u cot u du = - csc u + C. tan u du = ln | sec u| + C. sec u du = ln | sec u + tan u| + C. sinh u du = cosh u + C. cosh u du = sinh u + C. sech2 u du = tanh u + C. 1 a2 -u2 1 a2 +u2 sin u = cos u du . dx cos u = - sin u du . dx tan u = sec2 u du . dx sec u = sec u tan u du . dx cot u = - csc2 u du . dx csc u = - csc u cot u du . dx ln | sec u| = tan u du . dx ln | sec u + tan u| = sec u du . dx sinh u = cosh u du . dx cosh u = sinh u du . dx tanh u = sech2 u du . dx sin-1 u = tan-1 u = sec-1 u = du 1 . 1-u2 dx 1 du 1+u2 dx . du 1 . u u2 -1 dx du 1 . 1+u2 dx 1 du 1-u2 dx . du = sin-1 1 a u a + C. + C. u a du = tan-1 1 a u a 1 u u2 -a2 1 a2 +u2 1 a2 -u2 du = sec-1 u a + C. sinh-1 u = tanh -1 du = sinh-1 1 a + C. + C. du = tanh-1 u= u a ...
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This note was uploaded on 03/29/2008 for the course MATH 251 taught by Professor Skrypka during the Spring '08 term at Texas A&M.

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