Question

If `y=ln(sin(pi/2))`, then what is `dy/dx`?

Answer 1

0

Explanation:

Geometrical interpretation:

`y=ln sin (pi/2)=ln 1 = 0`. So, slope of this line, y'=(0)'=0

This equation represents the x-axis.

The slope of x-axis is 0.

Answer 2

I tried using your corrected version Miroslav.

Explanation:

If you needed `y=ln(sin(pi/x))`
you need to use the Chain Rule: derive first the argument, then the sine and finally the log:
`(dy)/(dx)=(-pi/x^2)*cos(pi/x)*1/sin(pi/x)=-pi/x^2*cot(pi/x)`