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 3.10 : Implicit Differentiation
13. Assume that \(x = x\left( t \right)\), \(y = y\left( t \right)\) and \(z = z\left( t \right)\) and differentiate \({x^2}\cos \left( y \right) = \sin \left( {{y^3} + 4z} \right)\) with respect to \(t\).
Differentiating with respect to \(t\) gives,
\[\require{bbox} \bbox[2pt,border:1px solid black]{{2x\,x'\cos \left( y \right) - {x^2}\sin \left( y \right)y' = \left( {3{y^2}y' + 4z'} \right)\cos \left( {{y^3} + 4z} \right)}}\]Note that because we were not asked to give the formula for a specific derivative we don’t need to go any farther. We could however, if asked, solved this for any of the three derivatives that are present.