D/ds s/sqrt(60s + 25)

[Appleton]

Homework Statement

d/ds s/sqrt(60s + 25)

Homework Equations

The Attempt at a Solution

d/ds s/sqrt(60s + 25) = d/ds s(60s + 25)^-1/2
if a = s(60s + 25)^-1/2
and b = (60s + 25)
da/db = -1/2s(60s +25)^-3/2
db/ds = 60
da/ds = -30s(60s +25)^-3/2

Any help much appreciated.

 

[CompuChip]

It looks like you are trying to use the chain rule, but that doesn't quite work here. The reason is that if you want to calculate da/db, you have to write a completely in terms of b, i.e. as (b - 25) / 60 * b^-1/2.

Note that after the rewriting in your first line (s (60s + 25)^-1/2) you have a product of two functions, i.e. you are looking for d/ds(a b) with a = s, b = (60s + 25)^-1/2