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anonymous
 one year ago
Find the derivative of f(x) = 6/x at x = 2.
anonymous
 one year ago
Find the derivative of f(x) = 6/x at x = 2.

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SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1Ok, lets rewrite the f(x) \(\large\color{black}{ \displaystyle f(x)=6(x)^{1} }\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1Apply the power rule. Can you do that?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1(YOu are to find the derivative, and then plug in x=2 into the derivative)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1is that your fnal answer?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1if so, then you are not correct....

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1Did you find the \(f'(x)\) /?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1Oh, what I mean by the power rule is: \(\large\color{black}{ \displaystyle \frac{d }{dx}x^n=nx^{n1} }\) where d/dx is jst a notation for taking the derivative.  But I guess you are doing by the first principles...

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0'm not really sure what you mean by power rule I have a formula for difference quotient f(h1)f(1)/h and I ended up with ([6/h1]6)/h

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0never heard of it this is precalc

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1yes, you are applying the following: \(\large\color{black}{ \displaystyle \lim_{h \rightarrow 0}\frac{f(x+h)f(x)}{h} }\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1\(\large\color{black}{ \displaystyle f'(x)= \lim_{h \rightarrow 0}\frac{f(x+h)f(x)}{h} }\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1YOu can use the power rule I posted, to at least check the work, but for now I guess we need this: \(\large\color{black}{ \displaystyle \lim_{h \rightarrow 0}\frac{f(x+h)f(x)}{h} }\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1Or, if you want to find \(f'(a)\) direclty: \(\large\color{black}{ \displaystyle f'(a)= \lim_{x \rightarrow a}\frac{f(x)f(a)}{xa} }\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1\(\large\color{black}{ \displaystyle f'(x)= \lim_{h \rightarrow 0}\frac{\dfrac{6}{x+h}\dfrac{6}{x} }{h} }\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1now, find the common denominator betwen 6/(x+h) and 6/x and subtract.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so would I multiply one side by x and the other by x+h

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1yes, fraction#1 by x on top and bottom, and fraction#2 (x+h) on top and bottom

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0pretty sure that's it thanks

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1\(\large\color{black}{ \displaystyle f'(x)= \lim_{h \rightarrow 0}\frac{\dfrac{6}{x+h}\dfrac{6}{x} }{h} }\) \(\large\color{black}{ \displaystyle f'(x)= \lim_{h \rightarrow 0}\frac{\dfrac{6x}{x(x+h)}\dfrac{6(x+h)}{x(x+h)} }{h} }\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1\(\large\color{black}{ \displaystyle f'(x)= \lim_{h \rightarrow 0}\frac{\dfrac{6x6(x+h)}{x(x+h)} }{h} }\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1\(\large\color{black}{ \displaystyle f'(x)= \lim_{h \rightarrow 0}\frac{\dfrac{6h}{x(x+h)} }{h} }\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yep that's what I got just forgot about the denomenator under the 6h

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1then divide top and bottom by h.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1\(\large\color{black}{ \displaystyle f'(x)= \lim_{h \rightarrow 0}\frac{\dfrac{6h}{x(x+h)}\color{red}{\div h} }{h \color{red}{\div h}} }\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1then you get: \(\large\color{black}{ \displaystyle f'(x)= \lim_{h \rightarrow 0}{~} \frac{6}{x(x+h)} }\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1yes, but you are leaving out that important limit.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so I just put 2 in for x

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1that limit that h=0, is an important component. So that when you simplify the expression, you then plug in h=0 (if you don;t get any undefined results for that)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1\(\large\color{black}{ \displaystyle f'(x)= \lim_{h \rightarrow 0}{~} \frac{6}{x(x+h)} =\frac{6}{x(x+0)}=\frac{6}{x^2} }\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1see what is that limit for? (it is a notation for the fact that h is 0)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1yes, that is right:

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0hey, thanks for the patience I'm kind of slow

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1Yes, don't forget that limit h>0 notation. it is important.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1So just an addition that in general: \(\large\color{black}{ \displaystyle f'(x)= \lim_{h \rightarrow 0}{~} \frac{f(x+h)f(x)}{h} }\) (Derivative a function f(x).) \(\large\color{black}{ \displaystyle f'(x)= \lim_{x \rightarrow a}{~} \frac{f(x)f(a)}{xa} }\) (Derivative a function f(x) evaluated at x=a.)
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