The document explains how to find the derivative of the function y = e^x/ln x using the quotient rule. It details the procedure by applying the formula g(x)f'(x) - f(x)g'(x) / g(x)^2 and simplifies the result. The final derivative is expressed as (e^x)(ln x - 1) / x(ln x)^2.

1. Find the derivative of the function y = e^x/lnx
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