Question

f(x)=ln(sinx) find f'(pi/4)
a. -.5 ln2
b. (sqrt2)/2
c. 0
d. 1
e. undefined
please help

Answer 1

f(x)=ln(sinx) find f'(pi/4)
let u=sin x
f '(x)=(1/sin x)(cos x)
=cos x/sin x=cot x
=1/tan x,
f'(pi/4) =1/tan(pi/4)=1