anonymous
  • anonymous
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
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
Could you show steps please, im really confused.
campbell_st
  • campbell_st
rewrite your function in index form \[f(x) = x^{-1}\] can you differentiate the function..?
across
  • across
You 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?

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anonymous
  • anonymous
Thanks for getting me started across. Ill see if I can simplify.
campbell_st
  • campbell_st
oops 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
anonymous
  • anonymous
Oh 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
  • campbell_st
well it simplifies to -1/x^2
campbell_st
  • campbell_st
so you need to check you value for a = 2
anonymous
  • anonymous
Oh, careless mistake. Thank you so much, this really helped.

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