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Section 3-9 : Chain Rule

15. Differentiate \(g\left( z \right) = 3{z^7} - \sin \left( {{z^2} + 6} \right)\) .

Hint : Don’t get too locked into problems only requiring a single use of the Chain Rule. Sometimes separate terms will require different applications of the Chain Rule, or maybe only one of the terms will require the Chain Rule.
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For this problem the first term requires no Chain Rule and the second term will require the Chain Rule. The derivative is then,

\[\require{bbox} \bbox[2pt,border:1px solid black]{{g'\left( z \right) = 21{z^6} - 2z\cos \left( {{z^2} + 6} \right)}}\]