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 2 years ago
Find the derivative of the given function at the indicated point.
f(x)=1/x,a = 2
f′(a)= lim (f(a+h)  f(a))/h
h > 0
 2 years ago
Find the derivative of the given function at the indicated point. f(x)=1/x,a = 2 f′(a)= lim (f(a+h)  f(a))/h h > 0

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MrOrbit
 2 years ago
Best ResponseYou've already chosen the best response.0Could you show steps please, im really confused.

campbell_st
 2 years ago
Best ResponseYou've already chosen the best response.0rewrite your function in index form \[f(x) = x^{1}\] can you differentiate the function..?

across
 2 years ago
Best ResponseYou've already chosen the best response.1You have that \(f(x)=1/x\) and are asked to compute its derivative at \(a=2\). Then\[f'(a)=\lim_{h\to0}\frac{1/(2+h)1/2}{h}.\]Can you simplify this and compute its limit?

MrOrbit
 2 years ago
Best ResponseYou've already chosen the best response.0Thanks for getting me started across. Ill see if I can simplify.

campbell_st
 2 years ago
Best ResponseYou've already chosen the best response.0oops 1st principles \[\lim_{h \rightarrow0} \frac{ \frac{1}{x + h}  \frac{1}{h}}{h}\] put the fractions in the numerator over a common denominator \[\lim_{h \rightarrow 0} \frac{\frac{x  (x +h)}{x(x+h)}}{h}\] so it can then be simplified to \[\lim_{h \rightarrow 0} \frac{\frac{h}{x(x + h)}}{h}\] or \[\lim_{h \rightarrow 0} \frac{h}{hx(x + h)}\] cancel the common factor and then substitute h = 0 to get the derivative

MrOrbit
 2 years ago
Best ResponseYou've already chosen the best response.0Oh I see, would it also simplify further to 1/x^2. Also at a=2, the deravitive of f(x) = 1/4 right?

campbell_st
 2 years ago
Best ResponseYou've already chosen the best response.0well it simplifies to 1/x^2

campbell_st
 2 years ago
Best ResponseYou've already chosen the best response.0so you need to check you value for a = 2

MrOrbit
 2 years ago
Best ResponseYou've already chosen the best response.0Oh, careless mistake. Thank you so much, this really helped.
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