Total differential
Multivariable and vector calculus · Mathematics
Study notes
Q: Approximate the change in z = x^2 y when (x,y) goes from (2,3) to (2.1, 2.9). fx = 2xy, fy = x^2. At (2,3): fx = 12, fy = 4. dx = 0.1, dy = -0.1. dz = 12(0.1) + 4(-0.1) = 1.2 - 0.4 = 0.8. True: z(2.1,2.9) = 4.41 times 2.9 = 12.789; z(2,3) = 12. Change 0.789 approx 0.8!