Gradient vs Directional Derivative
As you can see in the image I have shown Gradient of hill by blue vector. Vector red indicates direction of max slope. I have understood the gradient.
The problem I have is with directional derivative.
I have written equation for directional derivative.
Now, at (theta) = 0, directional derivative = gradient.
But if we increase theta, what happens then?
Blue vector shrinks? (reduction in magnitude?) (I think No.)
Or it it start pointing upward? (shown by red vector)
If yes! then does it have to be in same black colored vertical plane?
What is directional derivative visually? does it represent same vector that gradient does?
Please clarify. I tried lots of videos, it confused me more.