Derivate-recapitulare

 Considerând cadrul propice aplicării regulilor de derivare să ne reamintim:

 $\left(f+g\right)'=f'+g'$  

 $\left(f\cdot g\right)'=f'\cdot g+f\cdot g'$  

 $\left(\frac{f}{g}\right)^{'^{ }}=\frac{f'\cdot g-f\cdot g'}{g^2}$  

 $\left(\alpha\cdot f\right)'=\alpha\cdot f',\ unde\ \alpha\in R$  

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

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

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

 $Derivata\ functiei\ f\left(x\right)=\ln\ \frac{x-1}{x-2},\ pentru\ x>2$  

 $f'\left(x\right)=\frac{1}{\frac{x-1}{x-2}}=\frac{x-2}{x-1}$