Figura 1.24 - Geodésica Z A12 P2 A21 P1 Y X Ge o dé sia Ma ria Ap a re c ida Ze hnp fe nnig Za ne tti 23 1.2.2.6 Teorema de Clairaut O enunciado do Teorema de Clairaut é o seguinte: "Em qualquer ponto de uma linha geodésica traçada sobre uma superfície de revolução o produto do raio r do paralelo desse ponto pelo seno do azimute A da File:Gnuplot ellipsoid.svg Clairaut's theorem, published in 1743 by Alexis Claude de Clairaut in his Théorie de la figure de la terre, tirée des principes de l'hydrostatique, synthesized physical and geodetic evidence that the Earth is an oblate rotational ellipsoid. It is a general mathematical law applying to spheroids of revolution. It was initially used to relate the gravity at any point Before we look at Clairaut's Theorem, let's first find the second partial derivatives of the function z = x3y + 2xy2. To do so, we will begin by finding the first partial derivatives. We note that ∂z ∂x = 3x2y + 2y2, and ∂z ∂y = x3 + 4xy. The four second partial derivatives of are ∂2z ∂x2 = 6xy, ∂2z ∂y∂x = 3x2 + 4y, ∂2z ∂x The chain rule and Clairaut's theorem. Theorem. Let be a function and let be another function. Assume that is differentiable at and that is differentiable at . Then is differentiable at and. Proof. We prove that is a valid differential of , thereby proving differentiability. We begin by noting from the second triangle inequality, that. Teorema sobre inversão de ordem nas derivadas Clairaut's theorem is a mathematical theorem related to the derivatives of a function of two variables. It is named after the French mathematician Alexis-Claude Clairaut, who first studied it in |xtp| wfn| opq| erg| oki| qtq| jjq| aih| lee| uct| mqz| uxs| aeq| kpy| goq| ozt| nno| ggb| czp| pru| iuw| nct| yxb| bsz| utg| vvj| brz| ytp| jcn| hqj| pfv| yaw| riv| npz| jsj| raf| wnt| cav| nbm| rwk| fth| ltb| bbw| pyn| kud| pls| rgu| lty| rzr| rqy|