(a) Find the differential of the the function, y = ln(sin(x)) in its simplest form and (b) find the stationary point of the curve in the range 0 < x < 4.

a)For any function y = f(g(x)) the differential will take the form dy/dx = g'(x)f'(g(x)).(This is because of the chain rule,y = f(u), u = g(x)dy/du = f'(u), du/dx = g'(x)hence dy/dx = dy/du * du/dx = g'(x)f'(g(x)) )So for the equation y = ln(sin(x)) where f(u) = ln(u) and g(x) = sin(x). So using the formula above, dy/dx = cos(x)/sin(x) = 1/tan(x)b)Stationary point occurs when dy/dx = 0, so 1/tan(x) = 0,tan(x) = infinity,thinking about the graph of tan(x) it has a discontinuity at pi/2 where it's value tends to infinity, hence x = pi/2