Question

differantation
l'hopital tule
ln cosx/ln cos 3x

Answer 1

l 'hopital rule

Answer 2

are you trying to compute a limit?

Answer 3

yes

Answer 4

as \(x\to 0\) ?

Answer 5

yes

Answer 6

ok then you can take the derivative top and bottom separately
you get
\[\frac{3\cos(3x)\sin(3x)}{\cos(x)\sin(x)}\] if i am not mistaken

Answer 7

still get \(\frac{0}{0}\) so you have to do it again, using the product rule
then you can replace \(x\) by \(0\)

Answer 8

do you use quotient rule??to differentiate the equation

Answer 9

L'Hopital's rule says you just take the derivative of the top, and then take the derivative of the bottom. You do not use the quotient rule.

Answer 10

@satellite73 can u show me the step

Answer 11

The derivative of ln cos(x) is 1/cos(x) *(-sin(x)) Similarly, the derivative of ln cos(3x) is
1/cos(3x) *(-3sin(3x)).

This will give you a fraction over a fraction, which will simplify to what satellite73 posted. Unfortunately, you still end up with 0/0, so you have to use :L'Hopital's rule a second time.

Answer 12

thank u @calmat01