How to Use Implicit Differentiation for Second Derivatives

TL;DR

Implicit differentiation allows you to find the derivative of equations where y is a function of x by adding dy/dx when differentiating y variables. To find the second derivative, apply the quotient rule and substitute dy/dx back into the equation. This method is crucial for solving equations involving both x and y.

Transcript

in this video we're going to go over implicit differentiation so in this topic when you're dealing with implicit differentiation you're differentiating the equation with respect to x let's say if you want to find the derivative of y squared with respect to x this is going to be 2y times d y dx if you want to find the derivative of let's say r to th... Read More

Key Insights

• ❣️ Implicit differentiation differentiates equations with respect to x while treating y as a function of x.
• ❣️ When differentiating y variables, add dy/dx; when differentiating x, dx/dx cancels out.
• 🐞 The second derivative can be found using the quotient rule and replacing dy/dx.

Summary & Key Takeaways

• Implicit differentiation involves finding the derivative of an equation with respect to x, treating y as a function of x.

• When differentiating a y variable, always add dy/dx. When differentiating x, dx/dx cancels out.

• To find the second derivative, use the quotient rule and replace dy/dx with its value.