Hi guys, I am currently finishing my Calculus 1 course and gpt stuck in a couple of exercises that have the same principle.
Fo the first one, what I tried to do is put ln in both sides and use the ln rule ln(MN)= (ln M) + (ln N) and ln(M/N) = (ln M) - (ln N), but for some I'm getting it wrong... I THINK that my mistake is in the product rule in the numerator OR when I multiply the whole thing by Y or in that case, f (x).
\(\displaystyle \text{Let } f(x) = (x^4 + 7)^{ln(x)}\)
\(\displaystyle \text{Find }f^\prime(x) = \)
The second one is similar and I can't get it right. I got 1/x
(x^4+7)^(1/X - 1) BUT i GUESS IT'S WRONG...
\(\displaystyle \text{Let}\)
\(\displaystyle f(x) = \dfrac{x^7(x - 7)^4}{(x^2 + 8)^9}\)
\(\displaystyle \text{Use logarithmic differentiation to determine the derivative.}\)
\(\displaystyle f^\prime(x) = \)
Anyways guys really appreciate your help ad I really liked the forums. I'll try my best to help other people aswell!
Have a good day and thanks in advance!
EDIT: Guys I did the second one after trying it again! I had a problem with the chain rule but now I got it right
However, the first one is really annoying as I am trying to find a way to take ln (x) out of the exponent.
THANKS GUYS!
Fo the first one, what I tried to do is put ln in both sides and use the ln rule ln(MN)= (ln M) + (ln N) and ln(M/N) = (ln M) - (ln N), but for some I'm getting it wrong... I THINK that my mistake is in the product rule in the numerator OR when I multiply the whole thing by Y or in that case, f (x).
\(\displaystyle \text{Let } f(x) = (x^4 + 7)^{ln(x)}\)
\(\displaystyle \text{Find }f^\prime(x) = \)
The second one is similar and I can't get it right. I got 1/x
(x^4+7)^(1/X - 1) BUT i GUESS IT'S WRONG...
\(\displaystyle \text{Let}\)
\(\displaystyle f(x) = \dfrac{x^7(x - 7)^4}{(x^2 + 8)^9}\)
\(\displaystyle \text{Use logarithmic differentiation to determine the derivative.}\)
\(\displaystyle f^\prime(x) = \)
Anyways guys really appreciate your help ad I really liked the forums. I'll try my best to help other people aswell!
Have a good day and thanks in advance!
EDIT: Guys I did the second one after trying it again! I had a problem with the chain rule but now I got it right
However, the first one is really annoying as I am trying to find a way to take ln (x) out of the exponent.
THANKS GUYS!
Last edited:
