Definitions and Notations of Second Order Partial Derivatives For 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 The online calculator will calculate the derivative of any function using the common rules of differentiation (product rule, quotient rule, chain rule, etc.), with steps shown. It can handle polynomial, rational, irrational, exponential, logarithmic, trigonometric, inverse trigonometric, hyperbolic and inverse hyperbolic functions. Extra Practice: Find the derivative of the parametric function. Find 2nd derivative for #5 and #6. 1. x=t+l, y=t2 +3t, t = 1 2. x =cosÐ, y = 3sinÐ, 3COSû 3. x =cos3Ð, y = sin3Ð, = —3t, t ——1 5. x = 1 —t, y —t 3 —3t 6. X=4+2COSÐ, y = —1 + sine UX1-oCQ-.Vn.Q-a- So when you have the two critical points, then you want to apply the second derivative test to figure out for each critical point whether it's a saddle point, a minimum or a maximum. So we took our two critical points, (1, 1) and (0, 0), and at those points, we evaluated the second derivative. So A is the xx second derivative. B is the mixed ...