derivate -recapitulare Lesson Slides: 3 Slides (Grade 11)

3 Slides • 2 Questions

1

Derivate -recapitulare

2

formule:

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

3

Multiple Choice

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

1

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

2

$\frac{2}{x}$

3

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

4

$\frac{3}{2x}$

4

Multiple Choice

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

1

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

2

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

3

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

4

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

5

Rezolvări:

$2.\ \frac{\left(\ln x+1\right)'\cdot\left(\ln x-2\right)-\left(\ln x+1\right)\cdot\left(\ln x-2\right)'}{\left(\ln x-2\right)^2}=$
$\frac{\frac{1}{x}\left(\ln x-2\right)-\left(\ln x-1\right)\cdot\frac{1}{x}}{\left(\ln x-2\right)^2}=$
$\frac{\frac{1}{x}\ln x-\frac{2}{x}-\frac{1}{x}\ln x-\frac{1}{x}}{\left(\ln x-2\right)^2}=-\frac{3}{x\left(\ln x-2\right)^2}$

Derivate -recapitulare

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