Implicit differentiation question with inverse trig

In summary, the conversation is about finding the correct implicit derivative for a given equation. The person asking for help was advised to expand and simplify the equation under the square root and apply implicit differentiation. There is also mention of a "brute force" method and another method involving implicit differentiation. The person was then asked to share their work for further assistance.
  • #1
iwantcalculus
15
1

Homework Statement


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Homework Equations



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The Attempt at a Solution



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Note: by real solution I mean the correct implicit
derivative, not an actual real solution...
Please help![/B]
 
Last edited:
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  • #2
You can expand and simplify the expansion under the square root.
And you were asked to apply implicit differentiation. How would you do it?
Please, type in your work.
 
  • #3
ehild said:
You can expand and simplify the expansion under the square root.
And you were asked to apply implicit differentiation. How would you do it?
@iwantcalculus, there's the "brute force" way, which is how you are proceeding, and there's a different way that involves implicit differentiation. What's another way to write the equation you're starting with.
ehild said:
Please, type in your work.
Absolutely. Posting an image of your work doesn't let us insert a comment at a particular location where you might have gone wrong.
 

1. What is implicit differentiation?

Implicit differentiation is a method used in calculus to find the derivative of an equation that is not explicitly expressed in terms of a single variable. It is commonly used when the equation contains both dependent and independent variables, making it difficult to solve for the derivative using traditional methods.

2. What are inverse trig functions?

Inverse trigonometric functions are mathematical functions that undo the effects of trigonometric functions. They are commonly denoted with "arc" in front of the function symbol, such as arcsine (sin-1), arccosine (cos-1), and arctangent (tan-1).

3. How do you use implicit differentiation with inverse trig functions?

When using implicit differentiation with inverse trig functions, we first substitute the inverse function for the variable in the equation. Then, we apply the chain rule to differentiate the inverse trig function. Finally, we solve for the derivative of the original equation by substituting the inverse trig function back in for the variable.

4. What is the chain rule?

The chain rule is a rule in calculus that allows us to find the derivative of a composite function. It states that if a function f(x) is composed of two functions, g(x) and h(x), then the derivative of f(x) is equal to the derivative of g(x) multiplied by the derivative of h(x) with respect to x.

5. What are some common mistakes when using implicit differentiation with inverse trig functions?

Some common mistakes when using implicit differentiation with inverse trig functions include forgetting to substitute the inverse function for the variable, not applying the chain rule correctly, and not solving for the derivative of the original equation correctly. It is important to carefully follow each step and double check your work to avoid these mistakes.

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