B

9000071203

Část: 
B
Vypočtěte \(\int \frac{\cos 2x} {\sin ^{2}x}\, \mathrm{d}x\) na intervalu \((0;\frac{\pi}2)\).
\(- 2x -\mathop{\mathrm{cotg}}\nolimits x + c,\ c\in \mathbb{R}\)
\(\frac{\sin 2x} {-\frac{1} {3} \cos ^{3}x} + c,\ c\in \mathbb{R}\)
\(\mathop{\mathrm{tg}}\nolimits x - 2x + c,\ c\in \mathbb{R}\)

9000071207

Část: 
B
Vypočtěte \(\int \frac{6x} {(3x^{2}-4)^{2}} \, \mathrm{d}x\) na intervalu \(\left(\sqrt{\frac43};+\infty\right)\).
\(\frac{1} {4-3x^{2}} + c,\ c\in \mathbb{R}\)
\(\frac{3x^{2}} {x^{3}-12x^{2}+16x} + c,\ c\in \mathbb{R}\)
\(\frac{1} {(3x^{2}-4)^{2}} + c,\ c\in \mathbb{R}\)

9000070701

Část: 
B
Určete první derivaci funkce \(f\colon y = (2x - 5)^{-6}\).
\(f^{\prime}(x) = - \frac{12} {(2x-5)^{7}} ;\ x\in \mathbb{R}\setminus \left \{\frac{5} {2}\right \}\)
\(f^{\prime}(x) = - \frac{12} {(2x-5)^{7}} ;\ x\in \mathbb{R}\)
\(f^{\prime}(x) = - \frac{12} {(2x-5)^{5}} ;\ x\in \mathbb{R}\setminus \left \{\frac{5} {2}\right \}\)
\(f^{\prime}(x) = - \frac{12} {(2x-5)^{5}} ;\ x\in \left (\frac{5} {2};\infty \right )\)

9000070702

Část: 
B
Určete první derivaci funkce \(f\colon y = (x^{2} - 3x + 2)^{\frac{1} {2} }\).
\(f^{\prime}(x) = \frac{2x-3} {2\sqrt{x^{2 } -3x+2}};\ x\in \mathbb{R}\setminus \left \langle 1;2\right \rangle \)
\(f^{\prime}(x) = \frac{2x-3} {2\sqrt{x^{2 } -3x+2}};\ x\in \mathbb{R}\setminus \left (1;2\right )\)
\(f^{\prime}(x) = (4x - 6)\sqrt{x^{2 } - 3x + 2};\ x\in \mathbb{R}\setminus \left \langle 1;2\right \rangle \)
\(f^{\prime}(x) = (4x - 6)\sqrt{x^{2 } - 3x + 2};\ x\in \mathbb{R}\setminus \left (1;2\right )\)