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.
Show Solution
For this problem the first term requires no Chain Rule and the second term will require the Chain Rule. The derivative is then,
\[\require{bbox} \bbox[2pt,border:1px solid black]{{g'\left( z \right) = 21{z^6} - 2z\cos \left( {{z^2} + 6} \right)}}\]