Calculus III - Higher Order Partial Derivatives (Practice Problems)
Loading [MathJax]/jax/output/CommonHTML/fonts/TeX/fontdata.js
Paul's Online Notes
Paul's Online Notes
Home / Calculus III / Partial Derivatives / Higher Order Partial Derivatives
Hide Mobile Notice  
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 viewed in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device (you should be able to scroll/swipe to see them) and some of the menu items will be cut off due to the narrow screen width.

Section 13.4 : Higher Order Partial Derivatives

For problems 1 & 2 verify Clairaut’s Theorem for the given function.

  1. f(x,y)=x3y24y6x3 Solution
  2. A(x,y)=cos(xy)x7y4+y10 Solution

For problems 3 – 6 find all 2nd order derivatives for the given function.

  1. g(u,v)=u3v42uv3+u6sin(3v) Solution
  2. f(s,t)=s2t+ln(t2s) Solution
  3. h(x,y)=ex4y6y3x Solution
  4. f(x,y,z)=x2y6z32x6z+8y3x4+4z2 Solution
  5. Given f(x,y,z)=x4y3z6 find 6fyz2yx2. Solution
  6. Given w=u2e6v+cos(u64u+1) find wvuuvv. Solution
  7. Given G(x,y)=y4sin(2x)+x2(y10cos(y2))7 find Gyyyxxxy. Solution