Question

Problem set 1, Question 1F-7 d.
I'm not able to get the correct result. I get (-6a - 6at) in the numerator of the first fraction, where the result is (at * -6bt)
Isn't it correct that the product rule for 3 products is
f(x) = uvw
f'(x) = u v' w' + u' v w' + u' v' w.

Answer 1

The equation is
\[at(1+bt^2)^{-3}\]
I get the derivative for the last product
\[w' = [-3(1+bt^2)^{-4}(2) = -6(1+bt^2)^{-4} \]
\[a(1)w' + atw' + \frac{a(1)}{(1+bt^2)^3}\]
so I get
\[\frac{-6a}{(1+bt^2)^4}+\frac{-6at}{(1+bt^2)^4}+\frac{a}{(1+bt^2)^3}\]

What am I missing?

Answer 2

ahhh, see - sometimes it help to ask. I think I found my mistake. 'a' is of course just a constant. Let me try one more time

Answer 3

so, got the chain rule wrong (again!! :) ) \[w' = -3(1+bt^2)^{-4}(2bt) = \frac{-6bt}{(1+bt^2)^4}\]
And now I get the correct result.