How Do You Find The First And Second Derivative Of 2x Ln X Socratic
For the function z=f(x,y)=4x^2y^2 The gradient is For the function w=g(x,y,z)=exp(xyz)sin(xy), the gradient is Geometric Description of the Gradient Vector There is a nice way to describe the gradient geometrically Consider z=f(x,y)=4x^2y^2 The surface defined by this function is an elliptical paraboloid This is a bowlshaped surfaceYou can use Implicit differentiation to differentiate x 2 y 2 x y 2 = x y wrt x With implicit differentiation you differentiate each term on the both sides using standard rules If you encounter a y this becomes d y d x if you have a y 2 use the chain rule to get 2 y d y d x 2 x y x 2 d y d x 2 y 2 4 x y d y d x = 1 d y d x Rearrange
