Posted by **Tony** on Sunday, June 30, 2013 at 3:36pm.

what is the max value of y=x^22/10x^logx

- Maths -
**Steve**, Sunday, June 30, 2013 at 5:52pm
y = x^22 / 10x^logx

Nasty, but straightforward

Recall that d/dx (u^v) = v/u u^v u' + lnu u^v v'

I will assume by logx you mean lnx. If not, just recall that logx = lnx/ln10

d/dx x^lnx = (2/x lnx) x^lnx

So, using the quotient rule, we have

y' = 22x^21/(10x^logx) + x^22(20/x logx) x^logx

= 1/5 x^21/x^logx (11 - logx)

y'=0 when logx = 11, or x = e^11

y(e^11) = 1/10 e^121

whew - that's big!

## Answer this Question

## Related Questions

- ^Maths^ - If Logx-6 base3=2y and Logx-7 base2=3y, show that x^2-13x+42=72y
- math - I tried everthing but,I couldnt solve it. Please help me.the answer at ...
- college - FIND THE VERTEX THE LINE OF SYMMETRY THE MAX OR MIN VALUE OF THE ...
- algebra - If LOGx (A)=0.7 and LOGx (B) =0.5 how do I solve LOGx (B/A)
- Maths - f(x)=1+2cos2x Find min/max, period, general solution, sketch Period is ...
- Maths - If the minimum value of f(x)=x^2+18x+a is the same as the minimum value ...
- maths - X,4x+5 and 10x-5 are the first three terms of an arithmetic sequence. ...
- Math - Find the equation of the tangent line 5x^2+y^2=14 at (1,3). P.S: It's ...
- Calculus - Find the values for which f(x) = x^10-10x and if 0 (less than or ...
- Math - these are some problems i do not get any help is appreciated. These are ...