derivate -recapitulare

Derivate -recapitulare

formule:

•  $\left(\ln x\right)'=\frac{1}{x},\ x>0$  

•  $\left(\ln u\right)'=\frac{1}{u}\cdot u'$  

Multiple Choice

Calculați derivata funcției  $f\left(x\right)=\ln x+\ln2x+\ln3,\ x>0$  

•  $\frac{1}{x}+\frac{1}{2x}+\frac{1}{3}$  

•  $\frac{2}{x}$  

•  $\frac{1}{x}+\frac{1}{2x}$  

•  $\frac{3}{2x}$  

Multiple Choice

Calculați derivata funcției  $f\left(x\right)=\frac{\ln x+1}{\ln x-2},\ x>0,\ x\ne e^2$  

•  $-\frac{3}{x\left(\ln x-2\right)^2}$  

•  $\frac{3}{x\left(\ln x-2\right)^2}$  

•  $\frac{3}{x\left(\ln x-2\right)}$  

•  $-\frac{3}{x\left(\ln x-2\right)}$  

Rezolvări:

•  $2.\ \frac{\left(\ln x+1\right)'\cdot\left(\ln x-2\right)-\left(\ln x+1\right)\cdot\left(\ln x-2\right)'}{\left(\ln x-2\right)^2}=$  

•  $\frac{\frac{1}{x}\left(\ln x-2\right)-\left(\ln x-1\right)\cdot\frac{1}{x}}{\left(\ln x-2\right)^2}=$  

•  $\frac{\frac{1}{x}\ln x-\frac{2}{x}-\frac{1}{x}\ln x-\frac{1}{x}}{\left(\ln x-2\right)^2}=-\frac{3}{x\left(\ln x-2\right)^2}$