burgerandcheese
Junior Member
- Joined
- Jul 2, 2018
- Messages
- 85
The function f(x)=x−e−x has a real root which can be expressed in terms of the Lambert-W/Product Log Function:
f(x)=0⟹x=W(1)≈0.5671…
And since this root is a solution to the equation x=e−x, we can conclude that, at the point we're interested in, e−x=W(1)≈0.5. The gradiant (i.e. derivative) of e−x at this point is...?
The gradient of f+ g is the gradient of f plus the gradient of g: (f+ g)'= f'+ g' where I am using ' to indicate the gradient of a function.