Question

Hey needed a bit of help with derivatives of Ln and exponents. A sample problem im having a difficult time is...
f(t)= ln[(t^-2*(cos(t))^2))/(e^-t)^2]

Answer 1

the derivative of\[ln(f(x))=\frac{1}{f(x)}*f'(x)\]

Answer 2

ahh this will be a lot of typing, here we go...

Answer 3

\[\huge ln[\frac{t^{-2}*Cos^2t}{(e^{-t})^{2}}]'=?\]

Answer 4

Is that what you need to find?

Answer 5

yeah

Answer 6

So we follow the same formula, and keep in mind 1/a/b = b/a, so to find 1/f(t) we can just flip the fraction over.

Answer 7

okay i think i can see

Answer 8

try solving this, ill guide you in case of mistakes

Answer 9

so it becomes (e^t)^2/(t^-2*cos(t)^2)*

Answer 10

f'

Answer 11

im a bit stuck now. im trying to find the Derivative of (e^t)^2*(t^2)/cos^2(t)
am i on the right path?

Answer 12

yes you just need to find the derivative of the inside now