Question 1

1.  a) Одредити други извод функције $y=x^{4}-x^{2}$ . Срећан рад! Ј.М.

Accepted Answer

$y^{''}=12x^{2}-2$

Answer

$y^{''}=12x^{2}-4$

Answer

$y^{''}=12x^{2}+2$

Answer

$y^{''}=12x^{3}-2$

Question 2

б) $y=\cos x$

Accepted Answer

$y^{''}=-\cos x$

Answer

$y^{''}=-\sin x$

Answer

$y^{''}=-\sin x\cos x$

Answer

$y^{''}=\cos x$

Question 3

в) $y= tgx$

Accepted Answer

$y^{''}=\frac{2sinx}{cos^{3}x}$

Answer

$y^{''}=\frac{sinx-1}{cos^{3}x}$

Answer

$y^{''}=\frac{sinx}{cos^{3}x}$

Answer

$y^{''}=\frac{2sinx-1}{cos^{3}x}$

Question 4

г) $y= e^{2x}$

Accepted Answer

$y^{''}= 4e^{2x}$

Answer

$y^{''}= 8e^{2x}$

Answer

$y^{''}= e^{2x}$

Answer

$y^{''}= 2e^{2x}$

Question 5

д) $ y= x·arctg x$

Accepted Answer

$y^{''}= \frac{2}{\left( 1+x^{2}  \right) ^{2}}$

Answer

$y^{''}= -\frac{2}{\left( 1+x^{2}  \right) ^{2}}$

Answer

$y^{''}= -\frac{2x}{\left( 1+x^{2}  \right) ^{2}}$

Answer

$y^{''}= \frac{2x}{\left( 1+x^{2}  \right) ^{2}}$

Question 6

2. Одредити трећи извод функције $y= x^{2}·\ln \sqrt{x}$

Accepted Answer

$y^{'''}=\frac{1}{x}$

Answer

$y^{'''}=\frac{2}{x}$

Answer

$y^{'''}=\frac{1}{2x}$

Answer

$y^{'''}=-\frac{2}{x}$

Question 7

3. Одредити четврти извод функције $y= e^{-x}·\sin x$.

Accepted Answer

$y^{\left(  4 \right) }=-4e^{-x}sin x$

Answer

$y^{\left(  4 \right) }=-2e^{-x}cos x$

Answer

$y^{\left(  4 \right) }=2e^{-x}sin x$

Answer

$y^{\left(  4 \right) }=2e^{-x}cos x$

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