Question

If y=log tan (pie/4 +x/2) show that dy/dx = sec x

Answer 1

We know that tan (pie/4 +x/2) = sec x + tanx 
Now you can calculate the derivate to get dy/dx = sec x 

Answer 2

dy/dx={1/tan (pi/4+x/2)}sec^2 (pi/4+x/2).1/2

=1/2sec(pi/4+x/2)/sin (pi/4+x/2)

=1/{2sin (pi/4+x/2).cos (pi/4+x/2)}

=1/sin (pi/2+x)=1/cosx=secx

dy/dx=secx