1a)f(x)=2xˇ4+xˇ3-5, f´(x)=8xˇ3+3xˇ2
1b)f(x)= x + sin x, f)(x)=1-cos x
1c)f(x)=1/3xˇ3+xˇ(1/2), f´(x)=1/3.(-3).xˇ(-4)+1/2.xˇ(-1/2)=-xˇ(-4)+1/2.xˇ(-1/2)
1d)f(x)=x.cotg x, fˇ(x)=1.cotg x -x/sinˇ2x=cotg x -x/sinˇ2x
2a)f(x) = (-6x+2)(5-xˇ2)=-30x+6xˇ3+10-2xˇ2,f´(x)=18xˇ2-4x-30,f´(1)=-16
2b)f(x)=xˇ2/(x+5), f´(x)=(2x.(x+5)-2x)/(x+5)ˇ2=(2xˇ2+8x)/(x+5)ˇ2,f´(-4)=0
2c)f(x)=(3+x/2)ˇ1/2,f´(x)=1/2.(3+x/2)ˇ(-1/2).1/2=1/4. (3+x/2)ˇ(-1/2),f´(2)=1/8
3)f(x)=2.cos x + x, f´(x)=-2sinx +1,f´(x)=0, -2.sinx+1=0, sinx =1/2,x=pí/6+2k.pí i tože x =5/6pí+2k.pí
4)f(x)= 2/3.xˇ3-8x, f´(x)=2xˇ2-8, g(x)=2.xˇ(1/2),g´(x)=2.1/2.xˇ(-1/2)=xˇ(-1/2)
f´(x)/g´(x)=0, f´(x)=0, 2xˇ2-8=0,2xˇ2=8,xˇ2=4, /x/=2