Question

Sa se calculeze derivatele functiilor f:D⇒R

Am nevoie de macar 5 subpuncte de la E2 Si E3 sau macar 5 subpuncte de al un ex

Answer 1

E2.

a). x'= 1

(log in baza a din x)' =  1/(x*ln a)

f'(x)= 1/(ln 2)

b). (x^2)' = 2x

(rad din x)' = 1/(2 rad x)

f'(x)=2x/(2radx) = x/rad x = xradx/x = rad x

c). (sin x)'=cos x

(x)'=1

f'(x)= cos x

d). f(x)= -2x sinx

e). (a^x)' = a^x * ln a

(-1)'=0

f'(x)=(2^x * ln 2)(3^x * ln 3)

f).(ln x)'= 1/x

(log baza 2 din x)'= 1/(x*ln 2)

f'(x)= 2/x * 1/(x ln 2)= 2/(x^2*ln2)

g).  (rad x)' = 1/(2*rad x)

(rad de ordin 3 din x)' = 1/(3*rad x)

(x)'=1

f'(x)=( 1- 1/2radx)( 1+ 1/3radx)

E3. a). f'(x)= 1/(x^2)

b). f'(x)=(1' * x^2 -1 * x^2')/(x^2)^2 = (0-1*2x)/x^4 = -2x/x^4 = -2/x^3

c). f'(x)=1

d).f'(x)=1

e). f'(x)=(2x-1)/(2x+1)

f). f'(x)= 1/(2x-1)

g). f'(x)= cos x/(1-sinx)

h). f'(x)= -sin x/(1+cos x)

i). (tg x)' = 1/ cos^2 x

(sin x)'=cos x

f'(x)= 1/cos^2 x 1/cos x = 1/ cos^3 x

j). (ln x)' = 1/x

f'(x)= (1+1/x)/(1-1/x) =...