Finding a derivative – the steepness at a specific point on a curve – is an essential skill in your mathematical toolkit. When we know how a function changes with respect to a variable, we can solve acceleration, optimization, and many other types of problems. This lesson on the limit definition of the derivative explains how to find the gradient of any continuous and differentiable function at any point using Newton’s quotient (also called the difference quotient).

Dr. Hannah Fry is an associate professor in the mathematics of cities at the Centre for Advanced Spatial Analysis at University College London. She works with an interdisciplinary team to study many aspects of human behavior, such as shopping, relationships, transport, and urban crime.

Chapters:
0:00 Gradient At Specific Point
4:59 General Expression for Any Point
11:35 Summary

Learn more about optimization problems in this lesson:    • How to Solve Any Optimization Problem...  

This lesson is excerpted from Outlier’s Calculus I course. Learn more about this course and check out our full catalog at https://outlier.org

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