Find the derivative of the function y exlnxSolution y ex

Solution

y = e^x / ln x is the same thing as y = f(x) / g(x) To find the derivative, use g(x)f\'(x) - f(x)g\'(x) / g(x)^2 Therefore, (ln x) (e^x) - (e^x)(1/x) / (ln x)^2 f\'(e^x) = e^x g\'(ln x) = 1/x simplify and get (ln x)(e^x) - (e^x) / x(ln x)^2 or (e^x)(ln x - 1) / x(ln x)^2