(4tan(x))/x
find f '(x)
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