MHB 2.2.1 AP Calculus Exam .... derivative with ln

karush
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If $f(x)=7x-3+\ln(x),$ then $f'(1)=$
$a.4\quad b. 5\quad c. 6\quad d. 7\quad e. 8$

see if you can solve this before see the proposed solution
since
$$f'(x)=7+\dfrac{1}{x}$$
so then
$$f'(x)=7+\dfrac{1}{1}=7+1=8\textit{ is (e)}$$
 
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I "see" $7 + \dfrac{1}{x}$ as the derivative ...

here's one for you ...
 

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I will go with karush's question instead since my brain is closer to that level of question.
$$f'(1)=7+\frac11=7+1=8$$
The answer is D.
 
Monoxdifly said:
I will go with karush's question instead since my brain is closer to that level of question.
$$f'(1)=7+\frac11=7+1=8$$
The answer is D.

D is 7
 
karush said:
D is 7

Oops, sorry. I mean E.

Duh, even though I went with the easy question I still ended up misread the options. Sometimes I think I have ADD.
 
Well you are probably
Better at math than I am
 
karush said:
Well you are probably
Better at math than I am

Nah. Otherwise, I would do skeeter's question instead.
 
For skeeter's question use the fact that \frac{df^{-1}}{dx}= \frac{1}{\frac{df}{dx}$. We are asked to find g'(3) wheng(x)= f^{-1}{x)[/tex]. We know that g(f(x))= x and see that f(6)= 3. Since f'(6)= -2, g'(3)= -1/2, "(A)".

Actually, the fact that the only derivative we are given f'(6)= -2 is pretty much a "give away"!
 

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