Section 3.9 : Chain Rule
8. Differentiate \(g\left( x \right) = {{\bf{e}}^{1 - \cos \left( x \right)}}\) .
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 exponential functions remember that the outside function is the exponential function itself and the inside function is the exponent. The derivative is then,
\[\require{bbox} \bbox[2pt,border:1px solid black]{{g'\left( x \right) = \sin \left( x \right){{\bf{e}}^{1 - \cos \left( x \right)}}}}\]