Răspuns:
a) se aplica formula ln u=u `/u unde u=x²+5x
f `(x)=ln`(x²+5x)=(x²-5x)`/(x²-5x)=(2x-5)/(x²-5x)
f `(1)=(2*1-5)/(1²+5*1)=(2-5)/(1+5)= -3/6= -1/2
b)se aplica formula arcsin `u=u`/√(1-u²) unde u=x-1
f `(x)=(x-1) `/√[1-(x-1)²]=1/√[1-(x²-2x+1)]=
1/√(1-x²+2x-1)=1/√(-x²+2x)
f `(1)=1/√[-1²+2*1)=1/√(-1+2)=1√1=
1/1=1
Explicație pas cu pas:
