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I'm trying to resolve a derivate. the derivate of 1/x of f(2). i get ((1/(2+deltax))-1/2)/delta. But i really don't know how to do the Least common multiple of (1/(2+deltax)) - 1/2.

 Jun 8, 2014

Best Answer 

 #1
avatar+130182 
+5

Let's get the derivative, first.....then, we can "plug in"

lim(Δx →0)  [1/(x +Δx) - 1/x]/Δx  =

lim(Δx →0)  [x/[x(x +Δx)] - (x +Δx)/[x(x +Δx)]]/Δx  =

lim(Δx →0)  [x - (x +Δx)]/(Δx[x(x +Δx)]) =

lim(Δx →0)  [-Δx]/(Δx[x(x +Δx)]) =

lim(Δx →0)  -1/[x(x +Δx)]=

lim(Δx →0)  -1/[x2 +xΔx]  .....now, take the limit = -1/[x2 + 0] =

-1/x2

And evaluating this at x = 2, we have

-1/22  = -1/4

Note..you could go back and substitute "2" for "x"  in the limit stuff....you should arrive at the same answer without having to substitute at the end....!!!

  

 Jun 9, 2014
 #1
avatar+130182 
+5
Best Answer

Let's get the derivative, first.....then, we can "plug in"

lim(Δx →0)  [1/(x +Δx) - 1/x]/Δx  =

lim(Δx →0)  [x/[x(x +Δx)] - (x +Δx)/[x(x +Δx)]]/Δx  =

lim(Δx →0)  [x - (x +Δx)]/(Δx[x(x +Δx)]) =

lim(Δx →0)  [-Δx]/(Δx[x(x +Δx)]) =

lim(Δx →0)  -1/[x(x +Δx)]=

lim(Δx →0)  -1/[x2 +xΔx]  .....now, take the limit = -1/[x2 + 0] =

-1/x2

And evaluating this at x = 2, we have

-1/22  = -1/4

Note..you could go back and substitute "2" for "x"  in the limit stuff....you should arrive at the same answer without having to substitute at the end....!!!

  

CPhill Jun 9, 2014

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