Derivación implícita | Ejemplo 3

Takeaways

• 😀 Implicit differentiation is used when the variable y is not explicitly solved for, and it involves differentiating y as a function of x.
• 😀 The product rule is applied when differentiating terms involving both x and y, treating them as a product.
• 😀 When differentiating a product like 3x * y, the derivative involves using the product rule: (first factor) * (derivative of second factor) + (second factor) * (derivative of first factor).
• 😀 In implicit differentiation, always remember to include the derivative of y with respect to x (dy/dx) whenever y is involved in a term.
• 😀 The derivative of a constant, like 5, is zero, and the derivative of x terms follows standard rules (e.g., 2x^2 becomes 4x).
• 😀 When differentiating terms involving y (e.g., y^2), use the chain rule: the derivative of y^2 is 2y * dy/dx.
• 😀 After differentiating, group the terms involving dy/dx on one side of the equation and solve for dy/dx.
• 😀 Factor out dy/dx when possible to isolate it and make the final step of solving for it easier.
• 😀 The final result for dy/dx gives the derivative of y with respect to x, which is the main goal of implicit differentiation.
• 😀 Practice exercises are essential to mastering implicit differentiation, as shown in the video, where viewers are encouraged to try problems on their own.