What is implicit differentiation and can you give me an example?
An example of an AI chatbot conversation about implicit differentiation concepts and examples.
What is implicit differentiation and can you give me an example?
Implicit differentiation is a technique used to differentiate equations that define y implicitly in terms of x. For example, if you have the equation x^2 + y^2 = 1, you can differentiate both sides with respect to x.
How do you differentiate that equation step by step?
First, differentiate x^2 to get 2x. For y^2, use the chain rule: differentiate to get 2y(dy/dx). So, you have 2x + 2y(dy/dx) = 0.
What do I do next to solve for dy/dx?
You can isolate dy/dx by moving 2x to the other side: 2y(dy/dx) = -2x. Then, divide both sides by 2y to get dy/dx = -x/y.
Can you give me another example of implicit differentiation?
Sure! Consider the equation x^3 + y^3 = 3xy. You can differentiate it implicitly to find dy/dx.
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