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d/dx sq rt. lnx(x^2+X)find the derivatives.  The sq rt is continous over the entire...

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d/dx sq rt. lnx(x^2+X)

find the derivatives.  The sq rt is continous over the entire equation.

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`y = sqrt(lnx(x^2+x))`

Let `lnx(x^2+x) = u`

`y = sqrt(u)`

`(dy)/(dx) = 1/2 xx u^(-1/2) xx (du)/(dx)`

`(dy)/(dx) = 1/(2sqrt(u)) xx (du)/(dx)`

`(du)/(dx) = lnx(2x+1) + 1/x (x^2+x)`

`(du)/(dx) = lnx(2x+1) + (x+1)`

 

`(dy)/(dx) = 1/(2sqrt(lnx(x^2+x))) xx (lnx(2x+1)+x+1)`

 

 

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