Did i find the derivative correctly?

  • Thread starter dejan
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    Derivative
In summary, the conversation was about finding the derivative and second derivative of a given function. The person initially thought they had found the correct derivatives using the quotient rule, but the expert clarified that the derivative of a quotient is not equal to the quotient of the derivatives. They discussed alternative methods, such as using the product rule or substitution, to find the derivatives. The expert also mentioned that the function can be written as a product of two simpler functions. The person expressed their frustration but thanked the expert for their help.
  • #1
dejan
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Hi there,
Just wondering if i found dy/dx of (x+1)^2/1+x^2 = 2(x+1)/2x and also the second derivative d^2 y/dx^2=(x+1)/2
Is that correct?? I don't think it is.
 
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  • #2
dejan said:
Hi there,
Just wondering if i found dy/dx of (x+1)^2/1+x^2 = 2(x+1)/2x and also the second derivative d^2 y/dx^2=(x+1)/2
Is that correct?? I don't think it is.

No its not the derivative of a quotient is not equal to the quotient of the derivatives. Have you learned the quotient rule for differentiating these kinds of functions?
 
  • #3
Aww i have to use the quotient rule?? *sigh*
Well we didn't go that far:( More work! Thanks anyway!
 
  • #4
dejan said:
Aww i have to use the quotient rule?? *sigh*
Well we didn't go that far:( More work! Thanks anyway!

Well, you don't *have* to. You can use one of multiple methods,

for example, partial fraction decomposition into elementary functions with complex factors in the denominator.

Or even substitute [tex]x = tan \theta[/tex] simplify with trig identities first, then observe that [tex]\frac{dy}{dx} = \frac{\frac{dy}{d\theta}}{\frac{dx}{d\theta}}[/tex]

There are many way to skin a cat. :wink:
 
  • #5
Have you learned the product rule? The quotient rule is just a special case of the product rule.

Your function is a product of [tex](x+1)^2[/tex] and [tex](1+x^2)^{-1}[/tex]
 
Last edited:
  • #6
Yeah we've learned the product rule, chain and all...just that we have to graph that, but doing it without a graphics calculator.
I think i get it now.
 

1. How can I check if I found the derivative correctly?

To check if you found the derivative correctly, you can use the rules and formulas for finding derivatives and apply them to your solution. You can also plug in different values for the independent variable and see if your derivative matches the slope of the original function at those points.

2. What are some common mistakes when finding derivatives?

Some common mistakes when finding derivatives include forgetting to apply the chain rule, incorrectly applying the power rule, and forgetting to account for constants. It is also important to pay attention to the order of operations and simplify your final solution.

3. Can I use a calculator to find the derivative?

Yes, you can use a calculator to find the derivative, but it is important to understand the steps and rules involved in finding derivatives by hand. Using a calculator can help you check your work and save time, but it should not be relied on as the only method for finding derivatives.

4. Is there more than one way to find a derivative?

Yes, there are multiple methods for finding derivatives, such as using the limit definition, power rule, chain rule, and quotient rule. The method you use may depend on the complexity of the function and your personal preference.

5. What should I do if I am unsure if I found the derivative correctly?

If you are unsure if you found the derivative correctly, you can double check your work using the steps and rules for finding derivatives. You can also ask a classmate or teacher for help or use resources such as online calculators or textbooks for guidance.

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