Given that x = ln(sec(2y)) find dy/dx

x = ln (sec (2y))

The chain rule states that d/dy f (g (y)) = f'(g(y)). g'(y)

Here g(y) = sec(2y) so g'(y) = 2.sec(2y).tan(2y)

And f(y) = ln (y) so f'(y) = 1 / y

Thus dx/dy = (1 / sec(2y)) . (2.sec(2y).tan(2y)) = 2.tan(2y)