Quotient Rule

g(x) * f'(x) - f(x) * g'(x) / [g(x)]^2

F(x) = 4tan(x)/x

g(x) = x

g'(x) = d/dt[x] = 1

f(x) = 4tan(x)

f'(x) = d/dt[4tan(x)] = 4(secx)^2 * d/dt[x] = 4(secx)^2 * 1

Notice that d/dt tanx = (secx)^2

F'(x)= [x * 4(secx)^2 - 4tan(x) * 1] / x^2

= [ 4(x(secx)^2 - tan(x) ] / x^2