A graph of z = x 2 xy y 2 For the partial derivative at (1, 1) that leaves y constant, the corresponding tangent line is parallel to the xzplane A slice of the graph above showing the function in the xzplane at y = 1 Note that the two axes are shown here with different scales The slope of the tangent line is 3 The graph of this function defines a surface in Euclidean space ToFor a two variable function f(x , y), we can define 4 second order partial derivatives along with their notations Examples with Detailed Solutions on Second Order Partial Derivatives Example 1 Find f xx, f yy given that f (x , y) = sin (x y) Solution f xx may be calculated as follows f xx = ∂ 2 f / ∂x 2 = ∂(∂f / ∂x) / ∂x = ∂(∂ sin (x y) / ∂x) / ∂x = ∂(y cos (x yFor Example z=x 2y 2 can be modeled in three dimensional space, but personally I find it difficult to sketch!
Thomas Calculus 11e 8 1262 Pages 351 381 Flip Pdf Download Fliphtml5
