Question

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

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

Answer 2

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

Answer 3

how come? :(

Answer 4

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

Answer 5

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