Find the direction derivative of f(x,y)=x^3y^2 - 6y 
at (2,5) in the direction of <4,-3>.

Answer.
Let vector-v = <4, -3> then |v| = sqrt(16+9) = 5 so u-hat = <4/5, -3/5>
grad f = < 3x^2y^2, 2x^3y-6> and at (x,y) = (2,5)
grad f(2,5) = < 300, 74>
and finally
f_u(2,5) = 1200/5 - 222/5 = 978/5