Determining the Directional Derivative

[cse63146]

[SOLVED]Determining the Directional Derivative

Homework Statement

Find the following directional derivative of the following function in the direction of the given vector v

$$f(x,y) = x^5 y^3 + 8 \\\ v = (-4,3)$$

Homework Equations

$$\nabla_u f\left(x,y,z\right) = \frac{1}{\left|\bold{u}\right|}\left(\frac{\partial f}{\partial x}u_x + \frac{\partial f}{\partial y}u_y + \frac{\partial f}{\partial z}u_z\right)$$

The Attempt at a Solution

EDIT: nevermind, got it.

 

[lippyka]

\nabla_u f\left(x,y\right) = \frac{1}{\sqrt{(-4)^2 + 3^2}}\left(\frac{\partial f}{\partial x}(-4) + \frac{\partial f}{\partial y}3\right)\nabla_u f\left(x,y\right) = \frac{1}{5}\left(5x^4y^3(-4) + 8 \cdot 3\right)\nabla_u f\left(x,y\right) = -20x^4y^3 + 24