MAT 213 Lecture Notes - Lecture 15: Directional Derivative, Unit Vector, Farad

• School: Barry University
• Department: Math
• Course: MAT 213
• Professor: Staff

Document Summary

11. 6 directional derivatives and the gradient vector notes: sterling. Provide a generalization to each of the key terms listed in this section. When it comes to its (general) de nition, a function"s directional derivative while it"s at (x0, y0) while it"s in a unit vector of u = ha, bi is be the following while if its limit actually exists: Duf (x0, y0) = limh 0 h f (x0+ha,y0+hb) f (x0,y0) h i. Duf (x, y) = fx (x, y) a + fy (x, y) b. When it comes to its (general) proof, it would be rst to note g (a function) of h (a single variable) by the following: g (h) = f (x0 + ha, y0 + hb) Thanks to the derivative"s de nition, you can have the following limit and simpli cation: g (0) = limh 0 h f (x0+ha,y0+hb) f (x0,y0) h i.