Question

find f'(x) if f(x) = ln(sinx)

Answer 1

derivative of sinx divided by sinx

Answer 2

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

Answer 3

oops

Answer 4

cotx

Answer 5

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

Answer 6

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

Answer 7

got it?

Answer 8

oops? @satellite73

Answer 9

why cot x and not tan x

Answer 10

there was an erroneous tangent floating around,
it is gone

Answer 11

oh look, it came back!!

Answer 12

U can write it interms of tan x too

Answer 13

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

Answer 14

thanks