multivariate-calculus

The partial derivative of the function $$ f(x, y, z)=e^{1-x \cos y}+x z e^{\frac{-1}{\left(1+y^2\right)}} $$ with respect to $x$ at the point $(1,0, e)$ is

Let r = x 2 + y - z and z 3 - xy + yz + y 3 = 1. Assume that x and y are independent variables. At (x, y, z) = (2, -1, 1), the value (correct to two decimal places) of $${{\partial...

The directional derivative of $$f\left( {x,y} \right) = {{xy} \over {\sqrt 2 }}\left( {x + y} \right)$$ at $$(1, 1)$$ in the direction of the unit vector at an angle of $${\pi \ove...