1, y'=20x^3-6x+1 2,y'=(a+b)x^(a+b-1)
3, y'=1/2*x^(-1/2)+x^(-2) 4 , y=x^(-1/2)-x^(3/2), 所以:y'=-1/2x^(-3/2)-3/2*x^(1/2)
5, y=1-x^(1/2)-x^(-1./2)+1 y'=-1/2x^(-1/2)+1/2x^(-3/2)
6,y'=x-4x^(-2-1)=x-4x^(-3)
7, y'=2xlnx+x^2*1/x=2xlnx+x
8,y=(x-1+2)/(x-1)=1+2/(x-1) y'=-2(x-1)^(-2)
9,y'=-sinx+2xsinx+x^2cosx
10,y=3^xe^x y'=3^x *ln3 *e^x+3^xe^x=3^x e^x (ln3+1)
11 ,y=1/(xcosx)+xcosx/sinx
y=1/x*secx+xcotx
y'=-secx/x^2+tanxsecx/x+cotx-xcsc^2x
12 y=x^(1/2)cotx y'=1/2x^(-1/2)cotx-x^(1/2)csc^2x
13 y'=ln10*10^xsinx+10^xcosx-lnx/(ln10)
14 y'=5x^4+5^x * ln5
15 y'=4cosx-1/x+x^(-1/2)
16 y'=-(1+x+x^2)^(-2) *(2x+1)
17 y'=2xe^x+e^x*x^2+(x/(secx+cscx))'
y'=(x^2+2x)e^x+(secx+cscx-x(secxtanx-cscxcotx))/(secx+cscx)^2
18 y'=cotx-xcsc^2x+2cscxcotx
2
(1) y'=2xe^x+e^xx^2
y' x=1 =2e+e=3e
(2)y'=x*2^(-2x)'
y'=2^(-2x)+x(ln2*2^(-2x) *(-2))=2^(-2x)-2xln2*2^(-2x) x=1时:
y'=2^(-2)-2ln2*2^(-2)
y'=1/4-ln2 /2