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Some basic derivatives: f(x) f (x) f(x) f (x) xn nxn?1 ex ex ln(x). 1/x sin(x) cos(x) cos(x). ?sin(x) tan(x) sec2(x) cot(x). ?cosec2(x) sec(x) sec(x) tan(x) cosec(x). ?cosec(x) cot(x) tan?1(x). 1/(1 + x2) sin?1(x). 1/. v. 1 ? x2 for |x| < 1 cos?1(x). ?1/. v. 1 ? x2 for |x| < 1 sinh(x) cosh(x) cosh(x) sinh(x) tanh(x) sech2(x) coth(x). ?cosech2(x).
Page 1. ( ) -. ( ) = () = -. ( ) = . =( ). () - -. ( ? ) = +? ? ?. =( ). - =( ). =( ). ?. () = () = ? ?. () -. ( ) = ( ) =( ) = { +. == == ++. == , ,+. , , = +. ?= +.
List of Derivative Rules. Below is a list of all the derivative rules we went over in class. • Constant Rule: f(x) = c then f (x)=0. • Constant Multiple Rule: g(x) = c · f(x) then g (x) = c · f (x). • Power Rule: f(x) = xn then f (x) = nxn?1. • Sum and Difference Rule: h(x) = f(x)±g(x) then h (x) = f (x)±g (x). • Product Rule: h(x) = f(x)g(x) then h
DERIVATIVES AND INTEGRALS. + v] = u' + v'. [uv] = uv' + vu'. ||. = nun-lu' y2. = a = a = a a = a = a = a = a = a = a = a = a. Basic Differentiation Rules. 1. Icu] = cu vu' – uv'. 4. "] = *' w". 5. le] = 0. 6. Lu"] = mu-. 7. ) = 1 Basic Integration Formulas. 1. fastu) du = a?su) du. 2. ?tru) + stw)] du = frw) du 4 ?etu) du. 3. ?au = u + C. 4.
Integration formulas sin (. ) y D A. B x C. = +. ?. A is amplitude B is the affect on the period (stretch or shrink). C is vertical shift (left/right) and D is horizontal shift (up/down). Limits: 0. 0 sin sin. 1 cos lim. 1 lim. 0 lim. 0 x x x x x x x x x. ?>. ?>?. ?>. ?. = = =
Basic Differentiation Formulas www.math.wustl.edu/~freiwald/Math131/derivativetable.pdf. In the table below, and represent differentiable functions of ? ? 0РBС. @ ? 1РBС. B. Derivative of a constant .- .B ? ! Derivative of constant. ( ). We could also write. , and could use . .? .B .B w w. -? ? -. Р. Р-0С ? -0 the “prime
Differentiation Formulas d dx k = 0. (1) d dx. [f(x) ± g(x)] = f (x) ± g (x). (2) d dx. [k · f(x)] = k · f (x). (3) d dx. [f(x)g(x)] = f(x)g (x) + g(x)f (x) (4) d dx. (f(x) g(x). ) = g(x)f (x) ? f(x)g (x). [g(x)]. 2. (5) d dx f(g(x)) = f (g(x)) · g (x). (6) d dx xn = nxn?1. (7) d dx sin x = cos x. (8) d dx cos x = ? sin x. (9) d dx tan x = sec2 x. (10) d dx cot x = ? csc2 x.
Appendix G.1 ? Differentiation and Integration Formulas. G1. ?. Use differentiation and integration tables to supplement differentiation and integration techniques. Differentiation Formulas. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. Integration Formulas. Forms Involving. 1. 2. Forms Involving. 3. 4. 5. 6. 7. 8. 9. 10. 1. u a bu.
Standard forms; Standard substitutions; Integration by parts; Differentiation of an integral; Central difference notation; Approximating to derivatives; Interpolation: Everett's formula;. Numerical evaluation of There was discussion as to whether it should also include physical formulae such as Maxwell's equations, etc., but.
Note that all but the first one of these tend to be taught in a Calculus II class. u Substitution. Given. ( ). (. ) ( ) b a. f g x g x dx. ?. ? then the substitution. ( ). u g x. = will convert this into the integral,. ( ). (. ) ( ). ( ). ( ). ( ) b. g b a. g a. f g x g x dx. f u du. ?. = ?. ? . Integration by Parts. The standard formulas for integration by parts
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