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find from first principles the derivative of 5/(x^2+3)

Guest Mar 22, 2017
 #1
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5* (  1 /  [ (x + h)^2  + 3 ]     -  1 / [x^2 + 3]   )    /  h

 

5 * ( 1 / { x^2 + 2xh + h^2 + 3]   -  1  /  [x ^2 + 3] )  / h

 

5 *[ ( x ^2  + 3  -  x^2 - 2xh  - h^2  - 3 ]  /   [ h (x^2 + 2xh + h^2 + 3) (x^2 + 3) ]

 

5 *[ -2xh - h^2]  /  [ h (x^2 + 2xh + h^2 + 3) (x^2 + 3) ]

 

5 *h [ -2x - h] / [ h (x^2 + 2xh + h^2 + 3) (x^2 + 3) ]

 

5 [ -2x - h] / [  (x^2 + 2xh + h^2 + 3) (x^2 + 3) ]  ......  let  h →  0   and we have

 

[ - 10x ]   /    [ (x^2 + 3) (x^2 + 3]  =

 

-10x  / (x^2 + 3)^2

 

 

cool cool cool

CPhill  Mar 22, 2017

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