B

9000070807

Level: 
B
Differentiate the following function. \[ f(x) = \frac{x^{4} + 3} {x^{2}} + x^{3} \]
\(f'(x) = 3x^{2} + 2x - \frac{6} {x^{3}} ;\ x\in \mathbb{R}\setminus \{0\}\)
\(f'(x) = 6x^{2} - 2x - \frac{6} {x^{3}} ;\ x\in \mathbb{R}\setminus \{0\}\)
\(f'(x) = 3x^{2} + 2x + \frac{6} {x^{3}} ;\ x\in \mathbb{R}\setminus \{0\}\)
\(f'(x) = 6x^{2} - 2x + \frac{6} {x^{3}} ;\ x\in \mathbb{R}\setminus \{0\}\)

9000070808

Level: 
B
Differentiate the following function. \[ f(x)= \frac{x} {x + 1} \]
\(f'(x) = \frac{1} {(x+1)^{2}} ;\ x\in \mathbb{R}\setminus \{ - 1\}\)
\(f'(x) = - \frac{1} {(x+1)^{2}} ;\ x\in \mathbb{R}\setminus \{ - 1\}\)
\(f'(x) = \frac{x} {(x+1)^{2}} ;\ x\in \mathbb{R}\setminus \{ - 1\}\)
\(f'(x) = - \frac{x} {(x+1)^{2}} ;\ x\in \mathbb{R}\setminus \{ - 1\}\)

9000071203

Level: 
B
Evaluate the following integral on the interval \((0;\frac{\pi}2)\). \[ \int \frac{\cos 2x} {\sin ^{2}x}\, \mathrm{d}x \]
\(- 2x -\mathop{\mathrm{cotg}}\nolimits x + c,\ c\in \mathbb{R}\)
\(\frac{\sin 2x} {-\frac{1} {3} \cos ^{3}x} + c,\ c\in \mathbb{R}\)
\(\mathop{\mathrm{tg}}\nolimits x - 2x + c,\ c\in \mathbb{R}\)

9000071207

Level: 
B
Evaluate the following integral on the interval \(\left(\sqrt{\frac43};+\infty\right)\). \[ \int \frac{6x} {(3x^{2} - 4)^{2}}\, \mathrm{d}x \]
\(\frac{1} {4-3x^{2}} + c,\ c\in \mathbb{R}\)
\(\frac{3x^{2}} {x^{3}-12x^{2}+16x} + c,\ c\in \mathbb{R}\)
\(\frac{1} {(3x^{2}-4)^{2}} + c,\ c\in \mathbb{R}\)