(x+2)(x+3)2〔(x+2)(x+3) 十2(x+1)(x+3)+3(x1)(x+2) =2(x+2)(x+3)2(3x2+11x+9) 840.y=(sina+cosa)(rosa.sina) 解 y sIng(ICosa sina) t cosa(x sina cosa) rsin 2a+ cos 2a 841.y=(1+nxm)(1+mx"). 解y=mnxm-l(1+mx")+mnx”-1(1+nxm) mn(xm+x-I+(m+n)xm+n-13 842.y=(1-x)(1-x2)2(1-x3)3. 解F (1一x2)2(1-x3) 4z(1 9x2(1-x)(1-x2)2(1-x3)2 (1-x)2(1-x2)(1-x3)2(1+6x 十15x2+14x3) =-(1-x)(1+x)(1+2x)(1+4x 843.y1++x+x2) +-7x2)(1 解 +(x≠0) 16
844.证明公式 b t d 证 a(cx+ d-c(ax t (crtd) d- bc d (cx+4)2(cx+d)2 这里已暗设cx+d≠0 求下列函数之导函数: 845 2r 解 2(1 4 (1 a+x3(x1≠1 86y-1+2 解由于y= 1,故 2(1-2x) (1+xr) 解 (1-x)2(1+x)3-xt3(1+x)2(1-x)2-2(1-x)(1+x)3 77
1=+42 x)(1+x)x,(|x1≠1) 848 (2-x2)(3 解 (1-x)22x(3-x2)-3x2(2-x2)]+2(1-x)(2-x2)(3-x3) 12-6x-6x2+2x2+5x3x(x≠1) r) 849 (1+x) 解y=-(1=2)”(1+ (1+x)-(1 (1+x) (1-x)p1〔(p+q〕+(pq)x (1十 850.y= 解 〔px(1-x)qx(1-x)1(1+x)-x2(1 (1+ x(1-x) (1+x(p(+1)x-(+q 7-1)x2 (x≠:1) 851.y=x+√x+yx. 解 1十 852.y=x 18
√a2-x2+ 解y (|x|<|a|) 3x2(1-x3)+3x2(1+x ({x|≠1) 859.y √①+x2(x+√1+x2 解 (1+x2)(x+√1+x2) √1+x2+ 1++2x (1+x2) 860. Nx+ 解 +√ 20
1+ 1+2√x+4√x·√x+√x x+ (x>0) 861.y=√1+√1+yx 解 1+√1+ 3v(1+ 3 27√(1+yz)V(1+y+} (x≠0,x≠-1,x≠-8) 862. y= cos2x- sinx 解y 2sin2r- 2cosx - osx(1+sinx 863.y=(2-r)cosx 2xsinx ff y'=--2_]-(2-x2)sina+2sin. 2cos r sIn. 864.y= sin(cos r)cos(sinx)