Question

y = 3/(8+x). Calculate the 2nd and 3rd derivative. (show steps)

Answer 1

First you have to calculate the first derivative so to do that use the Quotient Rule \[\frac{(8 + x)(0) - (3)(1)}{(8 + x)^2}\]

Answer 2

I was told to use something called the Chain Rule.

Answer 3

The chain rule is used only when you have a composite function like f(g(x)).. What you have here is a quotient \[\frac{f(x)}{g(x)}\]

Answer 4

change to y = 3(8+x)^-1 and the chain rule becomes easier to see

Answer 5

Yeah you can do it that way but its not really necessary

Answer 6

I did the quotient rule, then I did it again, and the answer was wrong.

Answer 7

so y' = (-1)(3)(8+x)^-1-1
=-3(8+x)^-2

Answer 8

and use the same method for y'' and y'''

Answer 9

The first derivative is \[- \frac{3}{(8 + x)^2}\]

Answer 10

How did you get that as your derivative?

Answer 11

now it would be easier to use the chain rule so rewrite it as \[-3(8 + x)^{-2}\]

Answer 12

so the second derivative will be \[6(8 + x)^{-3} * 1\] or \[\frac{6}{(8 + x)^{3}}\]

Answer 13

and the third derivative would be \[- \frac{18}{(8+x)^{4}}\]