Derivatele funcțiilor elementare

 Derivata funcției $f:R\rightarrow R,\ f\left(x\right)=\left(x+1\right)\cdot e^x$ este:

•  $f'\left(x\right)=\left(x+2\right)\cdot e^x$  

•  $f'\left(x\right)=e^x$  

•  $f'\left(x\right)=x\cdot e^x$  

•  $f'\left(x\right)=\left(x-1\right)\cdot e^x$  

Derivata funcției $f:\left(0,\infty\right)\rightarrow R,\ f\left(x\right)=\frac{\ln\ x}{x}$  este:

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

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

•  $f'\left(x\right)=\frac{x\cdot\frac{1}{x}-\ln x\cdot1}{x^2}$  

•  $f'\left(x\right)=\frac{1}{x}$  

Dacă $f:\left[0,\infty\right)\rightarrow R,\ f\left(x\right)=\sqrt{x}$  atunci  $f'\left(9\right)$  este egal cu:

Fie $f:R\rightarrow\left[-1,1\right],\ f\left(x\right)=\sin x+\cos x$  , atunci  $f'\left(x\right)=$  

Dacă $f:R\rightarrow R,\ f\left(x\right)=2^x+x^2$ , atunci  $\lim_{x\rightarrow0}\frac{f\left(x\right)-f\left(0\right)}{x}$  este

• ln4

• 1

• ln2

• 0