partial derivatives

Let w = f (x, y), where x and y are functions of t. Then, according to the chain rule, dw/dt is equal to

Given a function $$f\left( {x,y} \right) = 4{x^2} + 6{y^2} - 8x - 4y + 8,$$ the optimal values of $$f(x,y)$$ is

For a scalar function $$f(x,y,z)=$$ $${x^2} + 3{y^2} + 2{z^2},\,\,$$ the gradient at the point $$P(1,2,-1)$$ is

The continuous function $$f(x, y)$$ is said to have saddle point at $$(a, b)$$ if

The derivative of $$f(x, y)$$ at point $$(1, 2)$$ in the direction of vector $$\overrightarrow i + \overrightarrow j $$ is $$2\sqrt 2 $$ and in the direction of the vector $$ - 2\o...