find the directional derivative of f at the point P in the indicated direction: f(xy) = xcos^2y p(2, pi/4)

Question

find the directional derivative of f at the point P in the indicated direction:
f(xy) = xcos^2y
p(2, pi/4)
< 5, 1>

anonymous · Answer

i just want to make sure i have my Fx and Fy correct.. i always have difficulties with cos/sin

Fx=cos^2y
Fy= -2xsin^2y

kinggeorge · Answer

$f_x$ looks correct, but $$f_y=-2x \cos(y)\sin^2(y)$$

anonymous · Answer

how come? :(

kinggeorge · Answer

$${\partial \over \partial y}\;\; x \cos^2(y)=2x \cos(y) \cdot \left( {\partial  \over \partial y} \cos(y)\right)=-2x \cos(y) \sin(y)$$I apologize. I shouldn't have squared sin.

anonymous · Answer

ohhhhh okay! cuz i have to derive the cos, that's right.. okay, cool, thank you!