Question

Sa se calculeze derivatele urmatoarelor functii :
a) f(x)=ln(x^2+5x), in x0=1
b) f(x)=arcsin(x-1), in x0=1

Answer 1

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: