Maths
posted by Tony .
what is the max value of y=x^22/10x^logx

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!
Respond to this Question
Similar Questions

college
FIND THE VERTEX THE LINE OF SYMMETRY THE MAX OR MIN VALUE OF THE FOLLOWING F(X)= X^2+10X+5 
math
I tried everthing but,I couldn't solve it. Please help me.the answer at the back is 40960.13 question: solve for x and check your solution. logx/log2 + logx/log4 + logx/log8 + logx/log16 = 25 THANK YOU FOR YOUR KIND HELP!!!! 
^Maths^
If Logx6 base3=2y and Logx7 base2=3y, show that x^213x+42=72y 
Calculus
Demand Equation. The price(in dollars),and the quantity x sold of a certain product, obey the demand equation. I can't figure out what price the company should charge to maximize revenue p=1/10x+150 R=p*x R=((1/10)*x+150)*x R=(1/10)*x^2+150x … 
logarithms maths
logx+logx+nlogx/n.plz solve with explanation thanks 
Maths
If logx^3=0.5,find the value of x. 
value
Logx + logy=4 logx +2logy=3 
maths need help log
if loxbase 2=k^2+2k what is the value of logx^3 base64 
math algebra
Sum the following term of progression to the last term, logx, logx^2 logx^3.... logx^120 
value
show that the sum of nterm of the progression is logx,logx^2,logx^3,logx^4is n(n+1)/2 logx