- #1
Destroxia
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Homework Statement
Find the directional derivative of ##f## at ##P## in the direction of ##a##.
## f(x,y) = 2x^3y^3 ; P(3,4) ; a = 3i - 4j ##
Homework Equations
## D_u f(x_0, y_0, z_0) = f_x(x_0, y_0, z_0)u_1 + f_y(x_0, y_0, z_0)u_2 ##
The Attempt at a Solution
## f_x (x,y) = 6x^2y^3##
## f_y (x,y) = 6x^3y^2##
## f_x (3,4) = 3456 ##
## f_y (3,4) = 2592 ##
## D_u f(x_0, y_0) = 3456u_1 +2592 u_2 ##
##u = \frac {a} {||a||} = \frac {\langle 3,4 \rangle} {5} = \langle \frac {3} {5}, \frac {4} {5} \rangle##
##D_u f(x_0, y_0) = 3456(\frac {3} {5}) + 2592(\frac {4} {5}) ##
##D_u f(x_0, y_0) = \frac {20736} {5}##
Now, my program wants this an exact number, no tolerance. It won't accept division either, so I don't know how to put in 20736/5. Just wondering if I made a mishap somewhere within the solution.