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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.
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For exponential functions remember that the outside function is the exponential function itself and the inside function is the exponent. The derivative is then,

\[\require{bbox} \bbox[2pt,border:1px solid black]{{g'\left( x \right) = \sin \left( x \right){{\bf{e}}^{1 - \cos \left( x \right)}}}}\]