Section 3.9 : Chain Rule
10. Differentiate \(u\left( t \right) = {\tan ^{ - 1}}\left( {3t - 1} \right)\) .
Hint : Recall that with Chain Rule problems you need to identify the “inside” and “outside” functions and then apply the chain rule.
Show Solution
For this problem the outside function is (hopefully) clearly the inverse tangent and the inside function is the stuff inside of the inverse tangent. The derivative is then,
\[\require{bbox} \bbox[2pt,border:1px solid black]{{u'\left( t \right) = \frac{3}{{{{\left( {3t - 1} \right)}^2} + 1}}}}\]