?For the following exercises, find the directional derivative using the limit definition

Chapter 4, Problem 261

(choose chapter or problem)

For the following exercises, find the directional derivative using the limit definition only.

\(f(x, y)=y^{2} \cos (2 x)\) at point \(P\left(\frac{\pi}{3},\ 2\right)\) in the direction of \(\mathbf{u}=\left(\cos \frac{\pi}{4}\right) \mathbf{i}+\left(\sin \frac{\pi}{4}\right) \mathbf{j}\)

Text Transcription:

f(x, y)=y^{2} \cos (2 x)

P\left(\frac{\pi}{3},\ 2\right)

\mathbf{u}=\left(\cos \frac{\pi}{4}\right) \mathbf{i}+\left(\sin \frac{\pi}{4}\right) \mathbf{j}