Why some math functions defy simple rearrangement
In short: When you can't isolate a variable, standard differentiation hits a wall. This video demonstrates how to find derivatives using implicit differentiation, a vital technique for complex equations and real-world applications like related rates.
Most introductory calculus focuses on explicit functions where y is clearly defined as f(x). However, many mathematical relationships cannot be easily rearranged into this form. Implicit differentiation solves this by treating y as an unknown function of x—notated as y(x)—and differentiating both sides of the equation simultaneously.
The video specifically walks through the derivative of y = cos(5x - 3y). To solve this, one must apply the chain rule and product rule because y is embedded within the expression. Mastering this method is essential for moving beyond basic algebra into complex calculus applications.
Opens the Intellect+ feed with this card first. Swipe up for the next one.
Sources
- Summary by Intellect · source: Implicit derivative of y = cos(5x - 3y) | Taking derivatives | Differential Calculus | Khan Academy
- Also: Calculus I - Implicit Differentiation
To cite this card, link to https://intellectplus.co.uk/app/ideas-implicit-derivative-of-y-cos-5x-3y-taking-derivatives-differ.
How we source, check and correct cards: Editorial standards.
General information, not professional advice. Spotted an error? Flag the card or see corrections and complaints.
Intellect Plus is a visual educational discovery platform for exploring fascinating facts and ideas. Brain Food, Not Brain Rot. What is Intellect Plus?
Related
More in Mathematics · More in Ideas & Philosophy · Latest · A–Z · All topics
