- #1

- 204

- 7

## 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.