Question

second derivative of 1/(x^2-x+6)

Answer 1

Hey

First Derivative :

$\frac{d}{dx} ( \frac{1}{ {x}^{2} - x + 6} )$

$= \frac{1}{({x}^{2} - x + 6)^{2} }(2x - 1)$

Second Derivative :

$= (2x - 1) \frac{d}{dx} (\frac{1}{({x}^{2} - x + 6)^{2} }) + (\frac{1}{{x}^{2} - x + 6 })^{2} \frac{d}{dx} (2x - 1)$
$= \frac{ {(2x - 1)}^{2} }{( {x}^{2} - x + 6)^{3} } + \frac{2}{ {( {x}^{2} - x + 6 )}^{2} }$

$= \frac{4 {x}^{2} - 4x + 1 + 2 {x}^{2} - 2x + 12}{ {( {x}^{2} - x + 6)}^{3} }$

$= \frac{6 {x}^{2} - 6x + 13 }{ {( {x}^{2} - x + 6 )}^{3} }$