Section 3.9 : Chain Rule
5. Differentiate \(G\left( x \right) = 2\sin \left( {3x + \tan \left( x \right)} \right)\) .
Hint : Recall that with Chain Rule problems you need to identify the “inside” and “outside” functions and then apply the chain rule.
For this problem the outside function is (hopefully) clearly the sine function and the inside function is the stuff inside of the trig function. The derivative is then,
\[\require{bbox} \bbox[2pt,border:1px solid black]{{G'\left( x \right) = 2\left( {3 + {{\sec }^2}\left( x \right)} \right)\cos \left( {3x + \tan \left( x \right)} \right)}}\]