Question

Sa se calculeze derivatele :

f(x)=(x+1)*2 la x
f(x)=x la a 3 lnx
f(x)=(2x+1)radical din x
f(x)=radical din x * 3 radical din x


Va rog ajutor !!!!!

Answer 1

f(x)'=(x+1)2ˣ=(x+1)'2ˣ+(x+1)2ˣ'=1× 2ˣ +(x+1)2ˣ ln x = 2ˣ (1+(x+1) ln x

f(x)= x³ ln x =
f(x'= (x³)' ln x+x³(ln x ) '=3x² ln x + x³ ×(1/x)= 3x² ln x +x²=x² (3 ln x +1)

f(x) = (2x+1) √x  deci    f(x)'= (2x+1)' √x + (2x+1) √x'=2 √x + (2x +1 ) ×(1/2√x)=(2√x·2√x +2x+1)/2√x = (4x+2x+1)/2√x=(6x+1)/2√x

f(x)=√x · 3√x  deci f(x)' = √x' · 3√x+√x · 3√x'=  dar (√x)'=1/2√x
=(1/2√x)· 3√x+√x ·3(1/2√x)=6/4