Derivace

Napsal uživatel ladislav.foltyn dne Po, 06/10/2019 - 14:11.
Project ID: 
6000000078
Accepted: 
Podoblast: 
Derivace funkce
Typ: 
Match
Layout: 
6x6
Question: 
Ke každé funkci $f$ přiřaďte správně její derivaci $f'$.
Questions Title: 
Funkce:
Answers Title: 
Derivace:
Question 1: 
$f(x)=\frac{\ln x}{x}$
Answer 1: 

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

Question 2: 
$f(x)=x^2\ln x$
Answer 2: 

$f'(x)=x\left(2\ln x+1\right)$

Question 3: 
$f(x)=\ln x+\frac{x^2}2$
Answer 3: 

$f'(x)=\frac{x^2+1}x$

Question 4: 
$f(x)=x\ln x^2$
Answer 4: 

$f'(x)=\ln x^2+2$

Question 5: 
$f(x)=\frac1x+\frac{\ln^2x}2$
Answer 5: 

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

Question 6: 
$f(x)=x\ln^2 x$
Answer 6: 

$f'(x)=\ln x\left(\ln x+2\right)$

Tex: 
%tiket 3270454 \NastavOT{2} \NastavOD{2}