EQUATION OF TANGENT TO A CURVE | Realitymath

Struggling with finding the equation of a tangent line when the curve is given implicitly? In this video, we dive deep into a classic calculus problem with not one, but *two full examples* to solidify your understanding!

We'll tackle these questions step-by-step:
1. Find the tangent to the curve `3y² + 6xy + 4x² - 2y = 5` at the point `P(3, 1)`.
2. Find the tangent to the curve `(3y²) - 2x² - 3x + 2y + 5 = 0` at the point `P(3, -3)`.

*What you'll learn in this tutorial:*
✅ The crucial first step: verifying the point lies on the curve.
✅ How to apply *implicit differentiation* to find `dy/dx` for equations where y is not isolated.
✅ Using the *product rule* within an implicit differentiation problem.
✅ How to evaluate the derivative at a specific point to find the **slope of the tangent line**.
✅ The final step: using the point-slope form to write the **equation of the tangent line**.

This is an essential skill for AP Calculus, A-Level Maths, and any first-year university calculus course. By the end of this video, you'll be a pro at finding tangent lines to implicitly defined curves!

*Practice makes perfect!* Pause the video and try each problem yourself before I go through the solution!

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*For the playlist:*
This video is part of our *Implicit Differentiation* playlist, where we cover everything from the basics to advanced applications. Be sure to check out the other videos for more practice problems and explanations!

*Subscribe* and hit the bell icon so you don't miss the next video in the series!

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