Page 4 - FORMULA DBM30043

DIFFERENTIATION
d
t. = 0,k is constant z. - nx'-t
dx&) *ru, lPower Rutel

3. *@*") = snvn-l 4. t g (x)) (x)
ax ftUrrl = f' (x) t s'
ddudu du du
5. = u u lProduct Rulef 5. !_A _rdi-=um
*luu) d.r* a, fQuotient Rute]
dx\u) D2
dv du dv d
7. [Chaii Rule) 8. -- (e') = e*
dr- d*^ d" a.x
d 1,
9. 10. , (ln x)
ftG*.u)-raxibxfi@r+o) ax x
d
11. b)l = + b) L2.
ftwro*+ *xfr{ax *(sinx) = cosr
13. d L4.
; (cos a') = - sin x {rrr^nx) = secz x
15. 16.
ftbrn{o*+ b)l : cos(ax + D xfr@x + b) fi[ror{o*+ b)l = - sin(ax + q xfi@x + b)

17. b)l = secz(ax + fi 18. d" du
{Lontor+ xfr@x + b) ;[sin"u] = nsin'-1 u x cos "";
19. u) : n cosn-7 u x xff 20.
fi[ror" -sinu ftUon" uf = n tan'-' u x sec2, "*

INTEGRATION
f exn+l | (ax * b\n+7
1. I axndx : ----:--;* c ;{n + -1} 2. + b)"dx -t c;{n +
J n*1. J@x = !1("-+, -1}

f
3. O O. = kx * c,k is constclnt 4.
-
I J I f(x)dx = F(b) F(a)
5. ji*=rnr*c 6. o* =lxur(ax + b) + c
v { ;*

7. e'+c 8. ,"'*o o* : eo*+b + c
[".a*: [ *x

I {
9. sinx ax = -cosx+c 10. ,or* dx = sinx I c

77. tanx+c
lr"r'xdx:
12. 7
I sin(ax t b) dx : - d . _xcos(ax*b)+c
VTlax + b)
t1
13.
J cos(ax +b) dx = O : _x sin (ax +b) + c
"
dilax-t b)
L4. '1
,rr'{o, + b) d.x
{
fi(ax + b)