Differentiation halp! (1 Viewer)

[ohexploitable]

 

[ohexploitable]

Oh wait... disregard that... I'm a fucking retard...

 

[Drongoski]

y = x^x

.: lny = ln(x^x) = xlnx

.: d/dx both sides: (1/y)dy/dx = x/x + lnx = 1 + lnx

,: dy/dx = y(1+lnx) = (1+lnx)x^x

 

[ohexploitable]

y = x^x

.: lny = ln(x^x) = xlnx

.: d/dx both sides: (1/y)dy/dx = x/x + lnx = 1 + lnx

,: dy/dx = y(1+lnx) = (1+lnx)x^x

Haha yeah, I got it immediately after I posted.

 

[gurmies]

y = x^x = e^ln(x^x) = e^(xlnx)

dy/dx = (1+lnx)*e^(xlnx)

= x^x*(1+lnx)

This negates the need to use implicit differentation.

 

[Drongoski]

y = x^x = e^ln(x^x) = e^(xlnx)

dy/dx = (1+lnx)*e^(xlnx)

= x^x*(1+lnx)

This negates the need to use implicit differentation.

Good one, gurmies.

 

[Entrant]

Implicit is still useful in 3U even though it is a 4U topic.
- Cambridge Year 11 3U textbook.