B

9000071207

Parte: 
B
Evalúa la siguiente integral en el intervalo \(\left(\sqrt{\frac43},+\infty\right)\). \[ \int \frac{6x} {(3x^{2} - 4)^{2}}\, \mathrm{d}x \]
\(\frac{1} {4-3x^{2}} + c,\ c\in \mathbb{R}\)
\(\frac{3x^{2}} {x^{3}-12x^{2}+16x} + c,\ c\in \mathbb{R}\)
\(\frac{1} {(3x^{2}-4)^{2}} + c,\ c\in \mathbb{R}\)

9000070701

Parte: 
B
Deriva la siguiente función. \[ f(x)= (2x - 5)^{-6} \]
\(f^{\prime}(x) = - \frac{12} {(2x-5)^{7}} ,\ x\in \mathbb{R}\setminus \left \{\frac{5} {2}\right \}\)
\(f^{\prime}(x) = - \frac{12} {(2x-5)^{7}} ,\ x\in \mathbb{R}\)
\(f^{\prime}(x) = - \frac{12} {(2x-5)^{5}} ,\ x\in \mathbb{R}\setminus \left \{\frac{5} {2}\right \}\)
\(f^{\prime}(x) = - \frac{12} {(2x-5)^{5}} ,\ x\in \left (\frac{5} {2},\infty \right )\)

9000070702

Parte: 
B
Deriva la siguiente función. \[ f(x) = (x^{2} - 3x + 2)^{\frac{1} {2} } \]
\(f^{\prime}(x) = \frac{2x-3} {2\sqrt{x^{2 } -3x+2}},\ x\in \mathbb{R}\setminus \left [ 1,2\right ] \)
\(f^{\prime}(x) = \frac{2x-3} {2\sqrt{x^{2 } -3x+2}},\ x\in \mathbb{R}\setminus \left (1,2\right )\)
\(f^{\prime}(x) = (4x - 6)\sqrt{x^{2 } - 3x + 2},\ x\in \mathbb{R}\setminus \left [ 1,2\right ] \)
\(f^{\prime}(x) = (4x - 6)\sqrt{x^{2 } - 3x + 2},\ x\in \mathbb{R}\setminus \left (1,2\right )\)

9000070703

Parte: 
B
Deriva la siguiente función. \[ f(x)= \sqrt{\sin x -\cos x} \]
\(f^{\prime}(x) = \frac{\sin x+\cos x} {2\sqrt{\sin x-\cos x}},\ x\in \left ( \frac{\pi }{4} + 2k\pi , \frac{5\pi } {4} + 2k\pi \right ),\ k\in \mathbb{Z}\)
\(f^{\prime}(x) = \frac{\sin x+\cos x} {2\sqrt{\sin x-\cos x}},\ x\in \left [ \frac{\pi }{4} + 2k\pi , \frac{5\pi } {4} + 2k\pi \right ] ,\ k\in \mathbb{Z}\)
\(f^{\prime}(x) = \frac{\sin x-\cos x} {2\sqrt{\sin x-\cos x}},\ x\in \left [ \frac{\pi }{4} + 2k\pi , \frac{5\pi } {4} + 2k\pi \right ] ,\ k\in \mathbb{Z}\)
\(f^{\prime}(x) = \frac{\sin x-\cos x} {2\sqrt{\sin x-\cos x}},\ x\in \left ( \frac{\pi }{4} + 2k\pi , \frac{5\pi } {4} + 2k\pi \right ),\ k\in \mathbb{Z}\)

9000070704

Parte: 
B
Deriva la siguiente función. \[ f(x) = \frac{1} {\cos x + 3x^{2}} \]
\(f^{\prime}(x) = \frac{\sin x-6x} {(3x^{2}+\cos x)^{2}} ,\ x\in \mathbb{R}\)
\(f^{\prime}(x) = \frac{6x-\sin x} {(3x^{2}+\cos x)^{2}} ,\ x\in \mathbb{R}\)
\(f^{\prime}(x) = \frac{\sin x-6x} {3x^{2}+\cos x},\ x\in \mathbb{R}\)
\(f^{\prime}(x) = \frac{6x-\sin x} {3x^{2}+\cos x},\ x\in \mathbb{R}\)