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derivative of sinx divided by sinx

\[\frac{d}{dx}[\ln(f(x))]=\frac{f'(x)}{f(x)}\] via the chain rule

oops

cotx

f(x) = ln(sinx)
y' = (1/sinx)(cosx)
y' = cosx/sinx
y' = cotx

f'(x)=d(lnsinx)/dx
= {d(ln sinx) /dsinx} * {dsinx /dx}
={1/sinx} *{cosx}
=cosx/sinx
=cotx

got it?

oops? @satellite73

why cot x and not tan x

there was an erroneous tangent floating around,
it is gone

oh look, it came back!!

U can write it interms of tan x too

BUT:
f'(x)= 1/tan x

thanks