Let $f(x,y) = xe^{x^2-y}$ and $P=(2,4)$.
(a) Calculate $\|\nabla f_P\|$.
(b) Find the rate of change of $f$ in the direction $\nabla f_P$.
(c) Find the rate of change of $f$ in the direction of a vector making an angle of $45^\circ$ with $\nabla f_P$.

Answers :
(a)
(b)
(c)