I will appreciate if someone could solve and explain me step by step the following problem:
Let be a differentiable in every point and satisfies the following:
1. for all .
2. The directional derivative of at point at direction equals to .
Yes I can see why you were confused I wrote the incorrect magnitude for the vector. It should be
Now we just need to compute two other partial derivatives. Using the chain rule we get that
This gives a system of 3 equations in three unknowns for the partial derivatives of the function at the point (1,2,6).