Implicit Differentiation Question - Stuck

In summary, the conversation was about someone struggling with Implicit Differentiation in their Calculus 12 online course. They shared their work so far and asked for help. Another person confirmed that the work was correct and suggested collecting the y' terms on one side. The person was grateful and felt they understood now.
  • #1
playdohh
5
0
Hi, I'm doing an online course for Calculus 12 and I have been struggling with Implicit Differentiation, hoping someone could maybe help me. Thanks.

I'm not positive I'm doing this right but maybe someone can point me in the right direction, this is what I have so far

y/(x-y) = x^2+1

y=(x^2+1)(x-y)

y' = (2x)(x-y)+(x^2+1)(1-y')

y' = 2x^2-2xy+x^2-x^2y'+1-y'

This is where I get stuck and am not sure if I'm making a mistake or know what to do next. Any help would be appreciated, thank you.
 
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  • #2
I just realized I posted this in the wrong section, Sorry. I'm not sure how to delete it.
 
  • #3
Hey playdohh.

What you've done is right. Just collect the y' terms on one side and you're done.
 
  • #4
awesome thanks, I think I got it now =)
 

1. What is implicit differentiation?

Implicit differentiation is a mathematical technique used to find the derivative of a function that is not explicitly expressed in terms of one variable. It is commonly used when the function contains both independent and dependent variables.

2. How is implicit differentiation different from regular differentiation?

Regular differentiation is used to find the derivative of a function that is explicitly expressed in terms of one variable. Implicit differentiation is used when the function cannot be solved for one variable, so the derivative is found with respect to the other variable.

3. When should implicit differentiation be used?

Implicit differentiation should be used when the equation of the function cannot be solved for one variable, making it difficult to use regular differentiation. This commonly occurs when the function is in the form of an equation rather than a single variable expression.

4. What are the steps for finding the derivative using implicit differentiation?

The steps for implicit differentiation are as follows:

  1. Take the derivative of both sides of the equation with respect to the desired variable.
  2. Use the chain rule and product rule as needed to simplify the derivative.
  3. Solve for the derivative by isolating it on one side of the equation.

5. What are some common mistakes to avoid when using implicit differentiation?

Some common mistakes to avoid when using implicit differentiation include:

  • Forgetting to use the chain rule when differentiating composite functions.
  • Forgetting to include the derivative of the independent variable when differentiating a dependent variable.
  • Incorrectly applying the product rule or chain rule.
  • Making algebraic errors when solving for the derivative.

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