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Directional Derivatives | What's the slope in any direction?

A directional derivative gives the slope in any particular direction, similar to partial derivatives which give the slope just in the x or y directions. We formally define directional derivatives by modifying the familiar limit definition of the derivative for when you move along some vector in the input space. Then we see a very nice feature that we can use the gradient vector grad(f) to make computing directional derivatives easy. If you have the gradient, you can get the directional derivative in the u direction with one easy dot product. **************************************************** YOUR TURN! Learning math requires more than just watching videos, so make sure you reflect, ask questions, and do lots of practice problems! **************************************************** ►Full Multivariable Calculus Playlist:    • Calculus III: Multivariable Calculus ...   **************************************************** Other Course Playlists: ►CALCULUS I:    • Calculus I (Limits, Derivative, Integ...   ► CALCULUS II:    • Calculus II (Integration Methods, Ser...   ►DISCRETE MATH:    • Discrete Math (Full Course: Sets, Log...   ►LINEAR ALGEBRA:    • Linear Algebra (Full Course)   *************************************************** ► Want to learn math effectively? Check out my "Learning Math" Series:    • 5 Tips To Make Math Practice Problems...   ►Want some cool math? Check out my "Cool Math" Series:    • Cool Math Series   **************************************************** ►Follow me on Twitter:   / treforbazett   ***************************************************** This video was created by Dr. Trefor Bazett. I'm an Assistant Teaching Professor at the University of Victoria. BECOME A MEMBER: ►Join:    / @drtrefor   MATH BOOKS & MERCH I LOVE: ► My Amazon Affiliate Shop: https://www.amazon.com/shop/treforbazett