Question

Use logarithmic differentiation to find the derivative of...

Answer 1

\[\frac{ {(e^-x)(cosx)^2} }{ x^2 + x +1}\]

Answer 2

supposed to be e to the negative x but i cannot get it format correctly.

Answer 3

okay well lets start by taking the natural log of the equation

Answer 4

is there a certain part that you are getting stuck at?

Answer 5

I tried to do it but I don't think I did something right. So we take the ln of both sides. to get ln y = ln (Equation)

Answer 6

yes I am pretty sure this is the way to do it

Answer 7

okay. so then what?

Answer 8

then we can use some of our knowledge of log rules to split up the log

log(x/y)=log(x)-log(y)

Answer 9

Yes. That's what I did.

Answer 10

then you can use log(xy)=log(x)+log(y) to further split up the log

Answer 11

or you could just leave it and use the derivative product rule, it is up to you

(I am referring to ln(e^(-1)(cosx)^2)

Answer 12

and then you can just use implicit differentiation on that equation and then solve for dy/dx

Answer 13

That is what I did. Thank you!!

Answer 14

great! also remember that you can replace y with the original equation if you don't want to leave it as y