Answer to Question #1692 in Calculus for radhs

Question

Use logarithmic differentiation to find the derivative of the function.
y = (tan(x))^(3/x)

Answer 1

d/dx( f(x)^g(x) ) = d/dx( e^( ln( f(x)^g(x) ))) = d/dx (e^(g(x)*ln(f(x)) = (g(x)ln(f(x))'*
(e^(g(x)*ln(f(x)) = (g'(x) ln(f(x)) + g(x)f'(x)/f(x))*(e^(g(x)*ln(f(x)) =
= (g'(x) ln(f(x)) + g(x)f'(x)/f(x)) f(x)^g(x)