3. What is the directional derivative of f(x,y) = 4x²y⁴ – 2x + 5 at the point (2,1) in the direction <-3,4>?

Using the notation of the gradient vector we can define the directional derivative in the direction of a unit vector u as,

The gradient vector of f(x,y) = 4x²y⁴ – 2x + 5 at the point (2,1) is,

Since the given vector <-3,4> is not a unit vector, let,

Thus, the directional derivative of f(x,y) at the point (2,1) in the direction of <-3,4> is,