Calculus
posted by Anonymous .
y=x^logbase5(x)

lny = log_5(x) lnx
= lnx/ln5 lnx
= 1/ln5 ln^2(x)
1/y y' = 1/ln5 * 2lnx * 1/x
y' = 2y lnx / x ln5
= 2lnx/ln5 x^(log_5(x)1)
= 2log_5(x) x^(log_5(x)1)
Respond to this Question
Similar Questions

Calculus
What is the use of Calculus? How is it use in jobs? 
PreCalculus/Calculus
I am too embarassed to ask this Calculus (really precalculus) question in tutoring, because I know I should know. Is the inverse of f(x)=3x1 actually f(x)=1/3x+1? 
Algebra
In an interview of 50 math majors, 12 liked calculus and geometry 18 liked calculus but not algebra 4 liked calculus, algebra and geometry 25 liked calculus 15 liked geometry 10 liked algebra but neither calculus nor geometry 2 liked … 
logarithms
evaluate each log. Ln e^3 logbase(1/1000) expand each log. logbase5 radical41/43 logbase7 8xy^4/3z^3 logbase5 4(7radicalxy^z) 
Calculus
What is the simplest solution to the Brachistochrone problem and the Tautochrone problem involving calculus? 
Calc
I need help solving this problem. logbase5(x+2)=2 
MATH
Consider the expression logbase5 a=n a) For what value(s) of a will n be a positive number? 
MATH
Consider the expression logbase5 a=n a) For what value(s) of a will n be a positive number? 
Finite Math
Fifty percent of students enrolled in calculus class have previously taken precalculus. Thirty percent of these students received an A for the calculus class, whereas twenty percent of the other students received an A for calculus. … 
Calculus
Hellp I have a calculus test on Monday 2. Calculate the slope of the tangent to the given function at the given point or value of x a. f(x)=3/x+1,P(2,1) b.h(x)=2/squareroot x + 5, P(4,2/3) ****Full solutions to please because I do …