How to find a slope when y isn't isolated
In short: When an equation links x and y in a way that makes it impossible to solve for one variable, standard differentiation fails. This video demonstrates how to navigate these complex curves using implicit differentiation.
The video walks through a practical application of implicit differentiation by calculating the slope of a tangent line for the curve $x^2 + (y-x)^2 = 28$ at the point where $x=1$.
By differentiating both sides of the equation with respect to $x$, students learn how to handle variables that are intertwined, a fundamental technique in AP Calculus AB. The lesson is contextualized by Bill Scott, a teacher at Phillips Academy who helped develop these specific Khan Academy lessons.
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Sources
- Summary by Intellect · source: Worked example: Evaluating derivative with implicit differentiation | AP Calculus AB | Khan Academy
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