Easy Derivative Q: 8 - sqr(29-4x+x^2)

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In summary, the conversation discusses finding the derivative of -8-sqrt(x^2-4x+29) and whether or not to use the chain rule. The consensus is that the chain rule cannot be used and the derivative is simply -1/2sqrt(x^2-4x+29).
  • #1
amac1212
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Homework Statement



- 8 - sqr(29-4x+x^2)

Homework Equations





The Attempt at a Solution



-8(-1/2)=4

4(29-4x+x^2)^-1/2(2x-4)?

am i on the right track?
 
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  • #2
I'm no expert,
if you have sqrt(u) you get 1/2sqrt(u)
I don't think you can do the chain rule because you have -8-sqrt(u),
so I think you have to take the derivative of -8 which is 0 - the derivative of sqrt(u).
 
  • #3
Remember that you can split up [tex]\frac{d}{dx}\left(-8-\sqrt{x^{2}-4x+29}\right)[/tex] to get [tex]\frac{d}{dx}\left(-8\right)-\frac{d}{dx}\left(\sqrt{x^{2}-4x+29}\right)[/tex]. From there you can apply the chain rule.
 
  • #4
You seem to have thought the -8 was MULTIPLYING the square root- it is not!
 

1. What is the derivative of the function 8 - sqr(29-4x+x^2)?

The derivative of the function is -4x/(29-4x+x^2).

2. How do you find the derivative of a function?

To find the derivative of a function, you need to use the rules of differentiation, such as the power rule, product rule, and chain rule. The derivative of a function is the slope of its graph at any given point.

3. Why is the derivative important in calculus?

The derivative plays a crucial role in calculus because it helps us understand how a function changes over time or distance. It also helps us to optimize functions and find the maximum and minimum values.

4. Can you explain the power rule for derivatives?

The power rule states that the derivative of a function with a constant raised to a power is equal to the constant multiplied by the power, and the power reduced by one. In other words, d/dx (x^n) = nx^(n-1).

5. What are some real-life applications of derivatives?

Derivatives have various real-life applications, such as in physics to calculate the velocity and acceleration of an object, in economics to determine the rate of change of a function, and in engineering to optimize designs and systems. They are also used in finance to calculate the rate of return on investments and in medicine to analyze data from medical tests.

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