If y=ln(sin(pi/2))y=ln(sin(π2)), then what is dy/dxdydx?

2 Answers
Dec 19, 2016

0

Explanation:

Geometrical interpretation:

y=ln sin (pi/2)=ln 1 = 0y=lnsin(π2)=ln1=0. So, slope of this line, y'=(0)'=0

This equation represents the x-axis.

The slope of x-axis is 0.

Dec 19, 2016

I tried using your corrected version Miroslav.

Explanation:

If you needed y=ln(sin(pi/x))y=ln(sin(πx))
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)dydx=(πx2)cos(πx)1sin(πx)=πx2cot(πx)