MAT 1332 Study Guide - Final Guide: Tangent Space, Jacobian Matrix And Determinant, Talking Lifestyle 1278
7 May 2015
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Mat1332: calculus for the life sciences ii - part 2. For functions with two or more variables, we don"t just have one derivative, but rather a derivative for each variable. Partial derivatives keep all other variables xed and look at the rate of change of only the variable of interest. = 2x + 3y f (x, y) = x2 + 3xy + y4 + 6. Eg) use the chain rule and product rule for g(x, y) = x2exy to nd g. Y sin(xy) y2 + 1 y2 + 1 (y2 + 1)( sin(xy)x) cos(xy)(2y) (y2 + 1)2. X(y2 + 1) sin(xy) 2y cos(xy) (y2 + 1)2. Eg) k(x, y, z) = eyz(x2 + z3). Geometric interpretation: for one-variable functions, df of the tangent line is (y y0) = f(cid:48)(x0)(x x0). dx is the slope of the tangent line at x. It"s similar for two variables, but now instead of a tangent line, we have a tangent plane.
