麻煩會的人幫我解以下微積分題目~謝謝

Question

1.Let f(x)= ln(ln(x)). Find the value of f\'(e).
2.Let f(x)=x^2x. Find the value of f\'(1).
3.Let f(x)=ln(3x^2+1+e^-x). Find the value of f\'(0).
4.Find the area of the region bounded by the curves x=4-y^2 and x=-3y.
5.Find the area of the region bounded bt the parabola x=y^2 and the line x-2y=3.

Answer 1

1. f(x)=ln(ln(x))f'(x)=(1/(ln(x)))(1/x)f'(e)=1/e2. f(x)= x2x ln(f(x))=2xlnx(1/f(x))f'(x) = (2x)(1/x)+2lnx = 2+2lnxf'(x)=x2x(2+2lnx)f'(1)=11(2+2ln1)=23. f(x)=ln(3x2+1+e-x)f'(x)=(1/(3x2+1+e-x))(6x-e-x)f'(0)=(1/2)(-1)= -1/24. x=4-y2 and x=-3y4-y2=-3yy2-3y-4=0(y+1)(y-4)=0, y=-1or 4∴交點為(3,-1), (-12,4)面積=∫-14 (4-y2)-(-3y) dy=∫-14 (4+3y-y2) dy= [4y+(3/2)y2-(1/3)y3]-14 = (16+24-(64/3))-(-4+(3/2)+(1/3))= (56/3)-(-13/6)= (112/6)+(13/6)= 125/65. x=y2 , x-2y=3交點(1,-1), (9,3)面積=∫-13 (2y+3)-(y2) dy= [y2+3y-(1/3)y3]-13= (9+9-9)-(1-3+(1/3))= 9+(5/3)= 32/3