1.2
f`(x)=(2+2x²-4x²)/(1+x²)²=(2-2x²)/(1+x²)²
f`(-3)=(2-18)/(1+9)²=-16/100=-0,16
1.3
f`(x)=(x-1)`*√(x²+1)+(x-1)*(√(x²+1))`=1*√(x²+1)+(x-1)*2x/(2√(x²+1))=
=√(x²+1)+x(x-1)/√(x²+1)=(x²+1+x²-x)/√(x²+1)=(2x²-x+1)/√(x²+1)
f`(0)=(0-0+1)/√(0+1)=1/1=1
1.4
y`=1/3*3cos²x*(-sinx)+sinx=sinx*(-cos²x+1)
y`(π/6)=sinπ/6*(-cos²π/6+1)=1/2*(-3/4+1)=1/2*1/4=1/8
1.5
f`(x)=4(x+1)/(x-1)*(x+1-x+1)/(x+1)²=4(x+1)/(x-1)*2/(x+1)²=8/[(x-1)(x+1)]=8/(x²-1)
f`(-3)=8/(9-1)=8/8=1
1.6
f`(x)=5/(2√e^5x)
f`(0)=5/(2√e)