Question

Find the derivative of y with respect to x, t or theta as appropriate
(b) y= ln((1-x)/(x+5)^3)

Answer 1

use quotient rule.

Answer 2

the answer is 2x-8 / (x+5)(1-x)
i tried the quotient rule but couldnt get the answer can u show how to do it? thanks

Answer 3

you break the ln into 2 parts. because it is a quotient. so the right side = ln ((1-x) - ln (x+5)^3 . and then take derivative as usual, part to part. try that way.

Answer 4

don't forget ln(x+5)^3 = 3ln(x+5). I checked and it works.

Answer 5

use some log laws to simplify the question

\[\ln(\frac{1-x}{(x + 5)^3}) = \ln(1 - x) - 3\ln(x + 5)\]

once you get the derivatives... to simplify you will need a common denominator of

(1 - x)(x + 5)

cross multiply for the numerators.