Paul's Online Notes
Home / Calculus I / Derivatives / Chain Rule
Show General Notice Show Mobile Notice Show All Notes Hide All Notes
General Notice

Small update to the site today that put the "Next Section" and "Previous Section" buttons in a slightly more obvious place. If they appear below (and slightly overlapping) the "Notes", "Practice Problems" and "Assigment Problems" buttons please clear your browsers cache. Some browsers (Chrome I'm looking at you.....) do not always look to the server to see if newer versions of some of the "background" files are available. Clearing your browsers cache will force them to get the newer versions.

Paul
January 27, 2020

Mobile Notice
You appear to be on a device with a "narrow" screen width (i.e. you are probably on a mobile phone). Due to the nature of the mathematics on this site it is best views in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device (should be able to scroll to see them) and some of the menu items will be cut off due to the narrow screen width.

### 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,

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