导数16基本公式推1

1、导数16基本公式推导t(cy = th g为常数)2 .(x+” 二 口- -。且a1)a xl na14 . (inx)=- x5.13) = alna, (a 6且3 * 1)6. (j) = /7. (s in x) = cos x8. fcosx/ 二- s in x,210, (cot x) = - c3c x11, (sec x) = sec xtan x12p (esc x)+ = - sec xcotx1 j. (arcs i n xj - |1 - x14. (arccos x)=15. arctan xy 二1 + x116. (arccot x)r =-1 * x9. (

2、tan x)h = sei xt (c),= 0, (c为常数)设函数=f(x)= 为常数上显然1 f5+ ax)=c,则有ay = f(x + &町-f(m) = c - c = 0ha y 0-7- - 0. o x x v i im 二 i in 0 = 0 10 k & 10即 = 02.（xa） 二 qx口 j （a 为实数）设函数y = /口为自然数），则有axa yi in i i m iax-0 * 汽x-*。n nxn(n - 1) n - 22xin * 1dx + + ()()n nxri nx3. (iogax5,=赤,(a)。且 a*1)a x设函数y = loax(

3、a 俎0* 1),则有ay = log3(x + ax) - logax - logil +14t (lnx)s =一x当口二焉中一瓯则有a”y /5. (a*) = ak|n ar (a )。且a 丰 1)已知v = a*是x = iq4v的反函数，而国=10”在(0, + 8)上单调可导.且 fl1logdy)=丰 0.“ yin a故在对应的区间(-81 + 8)内有即k (ex), = j当(/) = a*in 1a中自二 e时，有(j) - e。7. (s i n x)h = cos x设函数 = sin尤则有/ a a xay = s i n (x + ax) - s i n x

4、= 2co& |x + -jsa x s i n以t42=8邛 + 0a， x2 ) a xt y ii im i im (x +/3iim cos x + -i2a xin -i im = cc$c3 x.8, (cos x)si nxa kay- cos ya ka x-t- 8 in-2 )2a x sirt -iim sinfx + 4m-02i im & -* d *s i nx.29. (tan x) = sec x(tan x)pcos xi3inx)-cos x - s i nxicosx)-2 cos x2 cos x2 cos x2 sec xtan x.即tsecx)=

5、sec xtanx10. (cot x),二2csc x(cot jc ).2 si n(cos x )fs i n x - x(si n x)sin xgos xesc xsm xs in x即eotesc x11. (sec x),sec xtan xi gos x )i cos x2cos x2cos x-secxtanx即tsecx)，= sec xtanx12, (esc x)k-csc xcot x(csc x,csc kcot xsin k13, (arcs inx)=1 - x1(gos v)=arecas x)f =s i n ja rccos x)1， =(arc in x)f =is in y)11-.in2(arc.inx) =即i且res in x)1=14, (arccosx)=11 - x2即 arccos x15* (arctan x)h1 + x2v - (arctan x/ =-=(tany) sec y sec (arctanx) 1 + tan (arctanx)yp11 + x即(cretan =16. (arc