Posted by Adam on .
Find f'(7) for f(x)=6x^ln(x)

Calc 
MathMate,
Use 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.