B

9000070702

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

9000070703

Část: 
B
Určete první derivaci funkce \(f\colon y = \sqrt{\sin x -\cos x}\).
\(f^{\prime}(x) = \frac{\sin x+\cos x} {2\sqrt{\sin x-\cos x}};\ x\in \left ( \frac{\pi }{4} + 2k\pi ; \frac{5\pi } {4} + 2k\pi \right ),\ k\in \mathbb{Z}\)
\(f^{\prime}(x) = \frac{\sin x+\cos x} {2\sqrt{\sin x-\cos x}};\ x\in \left \langle \frac{\pi }{4} + 2k\pi ; \frac{5\pi } {4} + 2k\pi \right \rangle ,\ k\in \mathbb{Z}\)
\(f^{\prime}(x) = \frac{\sin x-\cos x} {2\sqrt{\sin x-\cos x}};\ x\in \left \langle \frac{\pi }{4} + 2k\pi ; \frac{5\pi } {4} + 2k\pi \right \rangle ,\ k\in \mathbb{Z}\)
\(f^{\prime}(x) = \frac{\sin x-\cos x} {2\sqrt{\sin x-\cos x}};\ x\in \left ( \frac{\pi }{4} + 2k\pi ; \frac{5\pi } {4} + 2k\pi \right ),\ k\in \mathbb{Z}\)

9000070704

Část: 
B
Určete první derivaci funkce \(f\colon y = \frac{1} {\cos x+3x^{2}} \).
\(f^{\prime}(x) = \frac{\sin x-6x} {(3x^{2}+\cos x)^{2}} ;\ x\in \mathbb{R}\)
\(f^{\prime}(x) = \frac{6x-\sin x} {(3x^{2}+\cos x)^{2}} ;\ x\in \mathbb{R}\)
\(f^{\prime}(x) = \frac{\sin x-6x} {3x^{2}+\cos x};\ x\in \mathbb{R}\)
\(f^{\prime}(x) = \frac{6x-\sin x} {3x^{2}+\cos x};\ x\in \mathbb{R}\)

9000070705

Část: 
B
Určete první derivaci funkce \(f\colon y =\ln (2x^{2} + 5x)\).
\(f^{\prime}(x) = \frac{4x+5} {2x^{2}+5x};\ x\in \left (-\infty ;-\frac{5} {2}\right )\cup \left (0;\infty \right )\)
\(f^{\prime}(x) = \frac{4x+5} {2x^{2}+5x};\ x\in \mathbb{R}\setminus \left \{-\frac{5} {2};0\right \}\)
\(f^{\prime}(x) = \frac{1} {2x^{2}+5x};\ x\in \left (-\infty ;-\frac{5} {2}\right )\cup \left (0;\infty \right )\)
\(f^{\prime}(x) = \frac{1} {2x^{2}+5x};\ x\in \mathbb{R}\setminus \left \{-\frac{5} {2};0\right \}\)

9000070706

Část: 
B
Určete první derivaci funkce \(f\colon y = \sqrt{x^{2 } + 3x}\).
\(f^{\prime}(x) = \frac{2x+3} {2\sqrt{x^{2 } +3x}};\ x\in \left (-\infty ;-3\right )\cup \left (0;\infty \right )\)
\(f^{\prime}(x) = \frac{2x+3} {2\sqrt{x^{2 } +3x}};\ x\in \left (-\infty ;-3\right \rangle \cup \left \langle 0;\infty \right )\)
\(f^{\prime}(x) = \frac{2x+3} {\sqrt{x^{2 } +3x}};\ x\in \left (-\infty ;-3\right )\cup \left (0;\infty \right )\)
\(f^{\prime}(x) = \frac{\sqrt{x^{2 } +3x}} {2x+3} ;\ x\in \left (-\infty ;-3\right \rangle \cup \left \langle 0;\infty \right )\)