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In the following problem $a,b,$ b,and c represent REAL NUMBERS. 
The derivative of $g\left(x\right)=log _{a}\left(bx\right)+cx^{2}is$ 
$○$ $g^{1}\left(x\right)=\right)dfrac\left(b\right)log _{-}a\left(bx\right)\right)\left(N1n$ $a\right)+2cx1\right)$ 
$○$ $\left(g\left(x\right)=\right)dtracb$ $loga\left(bx\right)+2c\times \right)Nln$ a}\) 
$○$ $g^{'}\left(x\right)=\left(dfraC\left(a\right)log _{-}a\left(bx\right)\right)\left(ln$ $\right)+2c\times 1\right)\right)$ 
$○$ $g^{1}\left(x\right)=\left(dfrac\left(b$ $log _{-}a\left(bx\right)\right)\left(ln$ $a1\right)$ 
$○$ $\left(\left(g^{1}\left(x\right)=b$ $log _{-}a\left(bx\right)+2cx1\right)$ 
$○$ $g\left(x\right)=\left(dfrac\left(b$ $log _{-}a\left(bx\right)\right)\left(1ln$ $a|+2c1\right)$ 

DESARROLLO DE TEMAS: 
$1$ $1$ $x$ 
La fracción que representa al número periódico $0.675675675$ es: 
a) $\right)$ $\dfrac {15} {37}$ b) $\dfrac {13} {37}$ c) $\dfrac {25} {37}$ d) $\dfrac {19} {37}$ $\right)$ $\dfrac {16} {37}$ 

$\left(int|imits$ $-0a1\left(1-\times n_{2}{\right)_{3}}^{n}$ 
$x^{A}3dx=7\right)$ 
$\left($ $frac\left(1\right)\left(40\right)\right)$ 
$\left($ $\left(troc\left(1\right)\left(35\right)\right)$ 
$\left(troc\left(1\right)\left(30\right)\right)$ 
$\left(tr0c\left(1\right)\left(25\right)\right)$ 

Which of the following rational numbers are 
equivalent? 
$0Ptionsy$ 
A \frac{5}{6}, \frac{30}{36} 
B $s\sqrt{rac\left(} -2\right)\left(3\right)\sqrt{1rac} \sqrt{4\right)16\right)4} $ 
C $s\sqrt{11aC\left(} -4\right)1-7b,\sqrt{1rac\left(16\sqrt{35\right)9} } $ 
D \frac{1}{2},\frac{3}{8} 

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