Differentiate x^2-(3x+1)/(x+2)

In summary, the conversation involves someone asking for help with a problem involving differentiation and providing a solution using LaTeX. The person giving the solution advises the use of parentheses in the equation to clarify the numerator and denominator.
  • #1
ttpp1124
110
4
Homework Statement
To be differentiated: x^2-3x+1/x+2
Relevant Equations
n/a
image4.jpeg

Is this correct?
 
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  • #3
Looks okay to me. Your handwriting of the math is a little hard for me to read, but it seems correct.

BTW, there is a good LaTeX tutorial at the top of the page under INFO/Help (and in the lower left of the edit window below). We encourage all users to use LaTeX when posting math at the PF, since it is so much easier for folks to read and respond to. For example, I think this is your problem and your final solution (you can use the Reply button to see how LaTeX was used to generate the equations):

[tex]y(x) = x^2 - \frac{3x+1}{x+2}[/tex]
[tex]\frac{dy(x)}{dx} = 2x - \frac{5}{(x+2)^2}[/tex]
 
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Likes benorin
  • #4
To be differentiated: x^2-3x+1/x+2
Don't write it this way. What you wrote would be interpreted to mean this:
##x^2 - 3x + \frac 1 x + 2##, which I'm sure isn't what you meant.
If you write a fraction using inline text, but sure to add parentheses whenever the numerator and/or denominator have multiple terms. You example should be written like this: x^2 - (3x + 1)/(x + 2).

Better yet, like this using TeX: ##x^2 - \frac{3x + 1}{x + 2}##
 
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Likes FactChecker
  • #5
Use parentheses whenever it would help to clarify how much is in the numerator and how much is in the denominator. Parentheses are free.
 

1. What is the first step in differentiating x^2-(3x+1)/(x+2)?

The first step is to use the power rule to differentiate x^2, which is 2x. Then, use the quotient rule to differentiate (3x+1)/(x+2).

2. How do you apply the power rule in differentiating x^2-(3x+1)/(x+2)?

The power rule states that the derivative of x^n is nx^(n-1). In this case, the derivative of x^2 is 2x.

3. What is the quotient rule and how is it used in differentiating (3x+1)/(x+2)?

The quotient rule states that the derivative of f(x)/g(x) is (g(x)f'(x) - f(x)g'(x)) / (g(x))^2. In this case, f(x) is 3x+1 and g(x) is x+2. Therefore, the derivative is ((x+2)(3) - (3x+1)(1)) / (x+2)^2.

4. Can you simplify the derivative of x^2-(3x+1)/(x+2)?

Yes, the derivative can be simplified to (x^2 - 5x - 2) / (x+2)^2.

5. What is the final result of differentiating x^2-(3x+1)/(x+2)?

The final result is 2x - (x^2 - 5x - 2) / (x+2)^2.

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