Implicit Differentiation with the Product Rule | Calculus

Calculus | Implicit Differentiation & Derivatives How do you find dy/dx when x and y appear together in the same equation? In this clip from Infinity’s Saturday Morning Math Help Live, Perla works through two Calculus problems involving implicit differentiation: x² + 3xy + y² = 12 and x²y + y³ = 10 Mr. Bru explains how to: • Differentiate both sides with respect to x • Remember that y is a function of x • Attach dy/dx when differentiating terms containing y • Use the Product Rule on terms such as xy and x²y • Collect all terms containing dy/dx • Factor out dy/dx • Isolate the derivative and simplify For the first equation: dy/dx = -(2x + 3y)/(3x + 2y) For the second equation: dy/dx = -2xy/(x² + 3y²) Implicit differentiation becomes much easier once you recognize that every time you differentiate y, the Chain Rule requires a factor of dy/dx. Want your own math question answered? Join us for free Saturday Morning Math Help Live and submit a question for a chance to have Mr. Bru work it out on the show. Submit your question here: https://forms.gle/AJg4dCph6uYvvR3KA Infinity - The Math Institute TheMathInstitute.com Math is just counting. Don’t get more math problems… Get solutions! #Calculus #ImplicitDifferentiation #Derivatives