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MrOrbit

  • 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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  1. MrOrbit
    • 2 years ago
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    Could you show steps please, im really confused.

  2. campbell_st
    • 2 years ago
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    rewrite your function in index form \[f(x) = x^{-1}\] can you differentiate the function..?

  3. across
    • 2 years ago
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    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?

  4. MrOrbit
    • 2 years ago
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    Thanks for getting me started across. Ill see if I can simplify.

  5. campbell_st
    • 2 years ago
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    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

  6. MrOrbit
    • 2 years ago
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    Oh I see, would it also simplify further to 1/x^2. Also at a=2, the deravitive of f(x) = 1/4 right?

  7. campbell_st
    • 2 years ago
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    well it simplifies to -1/x^2

  8. campbell_st
    • 2 years ago
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    so you need to check you value for a = 2

  9. MrOrbit
    • 2 years ago
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    Oh, careless mistake. Thank you so much, this really helped.

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