Calculate the differentiation

Calculate the differentiation of the logarithmic function

Exponential function

$s|ef\left(-1n$ $\left($ }\right)^{50}\ $\right)$ \ | | is\ equal\ to\ $S$ 
$s1S$ 
$S-1S$ 
$s2S$ 
$s50s$ 

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}\) 
$○$ $g^{'}\left(x\right)=\left(dfraC\left(a\right)log _{-}a\left(bx\right)\right)\left(ln$ $\right)+2c\times 1\right)\right)$ 
$○$ $g^{1}\left(x\right)=\left(dfrac\left(b$ $log _{-}a\left(bx\right)\right)\left(ln$ $a1\right)$ 
$○$ $\left(\left(g^{1}\left(x\right)=b$ $log _{-}a\left(bx\right)+2cx1\right)$ 
$○$ $g\left(x\right)=\left(dfrac\left(b$ $log _{-}a\left(bx\right)\right)\left(1ln$ $a|+2c1\right)$ 

The is the statement of the Mean Value Theorem from your $te\times tb00k$ 
$Tneoren$ $m4.5$ $Ne8n$ Value Theorem 
Let f be continuous over $leclose$ interval $\left(a.b\right)aod$ $i$ $eo$ $xd$ $csnlc$ $\left(ab\right)$ $mmd$ 
exists at least one point cE $\left(a.b\right)$ $si1dhtba$ 
$f^{'}\left(c\right)=\dfrac {f\left(b\right)-f\left(a\right)} {b-a}$ 
What is the geometric interpretation of the conclusion of the theorem? 
O The tangent line to the graph of $f\left(x\right)$ at $l\left(c1\right)$ is parallel to the 
secant line connecting $\left(a,f\left(a\right)\right)$ and 
$\left(b,f\left(b\right)\right)$. 
O The tangent line to the graph of $\left(f\left(lef\left(x\left(right\right)$ at $c$ is the secant line 
connecting $\left(a,f\left(a\right)\right)$ $ana$ $\left(b,f\left(b\right)\right)$. 
O The tangent line to the graph $of$ $\left(f\left(leF\left(x\left(right\right)\left(\right)at1\left(c1\right)is$ perpendicular to the 
secant line connecting $\left(a,f\left(a\right)\right)$ and 
A(\left(b,f\left(b\right)\right)\). 
O The tangent line to the graph of $\left(fleH\left(x\right)nght\right)\right)\right)$ $at$ $\left(c\right)\right)ishoizonta|$ 
$Tnere$ is more than one tangent line to the graph $0no$ $\left(flcf\left(x\right)night\right)\left($ $at1\left(c1\right)$ 

$8 \times $ 
$ = $ In $ \dfrac { E } { 8 } $ $ \left. \begin{array} { l } { \dfrac { 1 } { 3 } } \\ { \dfrac { 11 } { 3 } } \end{array} \right. $ $ \left. \begin{array} { l } { \dfrac { 1 } { 1 } } \\ { \dfrac { 1 } { 1 } } \end{array} \right. $ and $ \left. \begin{array} { l } { δ } \\ { 8 } \end{array} \right. $ 
Find the length of PR. $ \bar { I } $ 
$0$ 
$ \bar { u } $ 
$2$ $ = $ $ \| = $ 

Determine Value $f _{ 1 } t$ $ - \quad $ such that 
$ | A | = \left. \begin{array} { cc } { t - 2 } & { 4 } & { 4 } \\ { 1 } & { 0 + 1 } & { - 2 } \\ { 0 } & { 0 } & { - 4 } \end{array} \right| = 0$ 

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

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