I have been informed that on March 7th from 6:00am to 6:00pm Central Time Lamar University will be doing some maintenance to replace a faulty UPS component and to do this they will be completely powering down their data center.
Unfortunately, this means that the site will be down during this time. I apologize for any inconvenience this might cause.
Paul
February 18, 2026
Section 3.12 : Higher Order Derivatives
4. Determine the fourth derivative of \(\displaystyle f\left( w \right) = 7\sin \left( \frac{w}{3} \right) + \cos \left( {1 - 2w} \right)\)
Show All Steps Hide All Steps
Start SolutionNot much to this problem other than to take four derivatives so each step will show each successive derivative until we get to the fourth. The first derivative is then,
\[f'\left( w \right) = \frac{7}{3}\cos \left( \frac{w}{3}\right) + 2\sin \left( {1 - 2w} \right)\] Show Step 2The second derivative is,
\[f''\left( w \right) = - \frac{7}{9}\sin \left( \frac{w}{3} \right) - 4\cos \left( {1 - 2w} \right)\] Show Step 3The third derivative is,
\[f'''\left( w \right) = - \frac{7}{{27}}\cos \left(\frac{w}{3}\right) - 8\sin \left( {1 - 2w} \right)\] Show Step 4The fourth, and final derivative for this problem, is,
\[\require{bbox} \bbox[2pt,border:1px solid black]{{{f^{\left( 4 \right)}}\left( w \right) = \frac{7}{{81}}\sin \left( \frac{w}{3}\right) + 16\cos \left( {1 - 2w} \right)}}\]