Paul's Online Notes
Paul's Online Notes
Home / Calculus I / Applications of Derivatives / Differentials
Show Mobile Notice Show All Notes Hide All Notes
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 4.12 : Differentials

For problems 1 – 3 compute the differential of the given function.

  1. \(f\left( x \right) = {x^2} - \sec \left( x \right)\) Solution
  2. \(w = {{\bf{e}}^{{x^{\,4}} - {x^{\,2}} + 4x}}\) Solution
  3. \(h\left( z \right) = \ln \left( {2z} \right)\sin \left( {2z} \right)\) Solution
  4. Compute \(dy\) and \(\Delta y\) for \(y = {{\bf{e}}^{{x^{\,2}}}}\) as x changes from 3 to 3.01. Solution
  5. Compute \(dy\) and \(\Delta y\) for \(y = {x^5} - 2{x^3} + 7x\) as x changes from 6 to 5.9. Solution
  6. The sides of a cube are found to be 6 feet in length with a possible error of no more than 1.5 inches. What is the maximum possible error in the volume of the cube if we use this value of the length of the side to compute the volume? Solution