Find the directional derivative of f(x, y) = 2ye3x + (x − 1) sin(y − 2) at P0(0, 2) in the direction of v = 5i − 12j.

Question

Find the directional derivative of f(x, y) = 2ye^3x + (x − 1) sin(y − 2) at P₀(0, 2) in the direction of v = 5i − 12j.

Answer 1

The directional derivative of any particular function is the gradient vector as a dot product with the unit vector of the direction.

1. transfer the <5,-12> into a uint vector
2. find the partial derivative of the function with respect to x, and then do another one with respect to y
3. finally complete the dot product of the two vectors and you will get the directional derivative
4. plug in your values

If you need help with one of the particular steps let me know!