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January 26, 2015

January 26, 2015

Posted by **Adam** on Thursday, November 4, 2010 at 12:24am.

- Calc -
**MathMate**, Thursday, November 4, 2010 at 9:19amUse chain rule.

Let

y=6x^{ln(x)}

take log on both sides:

ln(y) = ln(6)+ln(x)*ln(x)

ln(y) = ln(6) + ln²(x)

differentiate both sides w.r.t. x

(1/y)y' = 0 + 2ln(x)*(1/x)

y' = dy/dx

= y*2ln(x)*(1/x)

= 6x^{ln(x)}*2ln(x)*(1/x)

= 12x^{ln(x)-1}*ln(x)

Check my calculations.

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