Partial Derivatives, Schemes and Mind Maps of Differential Equations

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Partial Derivatives

a Partial Derivatives Consider the same surface cut by two different planes. In a it is cut by y = y 0 , in b it is cut by x = x 0. The curve of intersection in a goes through plane RPQ and in b through plane MPL. Each of those curves has a tangent line associated with it at point P. Each tangent line has a steepness associated with it and that should make us think about what? b

Notation If z = f(x,y) , then partial derivative of f with respect to x partial derivative of f with respect to y EX 2 If z = x^2 y + cos(xy) - 2 , find and.

EX 3 Find the 'slope' of the tangent line to the curve of intersection of this surface and the plane x = 1 at the point. The 'slope' here refers to the change in z over the change in y.

Higher Order Partial Derivatives EX 5 Find all four second partial derivatives for f(x,y) = (x^3 + y^2 )^5.

EX 6 Find all four second partial derivatives for f(x,y) = tan-^1 (xy).