Derivative of c= (2p/q)-1/2: Step-by-Step Solution and Tips

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In summary, a derivative is a fundamental concept in calculus used to measure the rate of change of a function. It has many applications in various fields and can be found using different techniques. The derivative also represents the slope of a graph at a specific point and can be negative or positive depending on the direction of the function.
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babypudding
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Homework Statement



Find dc/dp and dc/dq.

Homework Equations



c= (2p/q)-1/2

The Attempt at a Solution



I just want to make if I'm right. I got...
dc/dp = (2/q)-1/2

dc/dq = [-2p/(q^2)] -1/2

Thanks.
 
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  • #2


Hi,
There is an error in your use of the chain rule:
[tex] \frac{dc}{dp}=-\frac{1}{2}\left(\frac{2p}{q}\right)^{-\frac{3}{2}}\cdot\left(\frac{2q-0}{q^2}\right)[/tex]
then simplify.

Same thing for dc/dq:
[tex]\frac{dc}{dq}=-\frac{1}{2}\left(\frac{2p}{q}\right)^{-\frac{3}{2}}\cdot\left(\frac{0-2p}{q^2}\right)[/tex]
then simplify.
 
Last edited:

1. What is a derivative?

A derivative is a fundamental concept in calculus that represents the rate of change of a function with respect to its independent variable. In simpler terms, it measures how much a function changes when its input changes.

2. Why is understanding derivatives important?

Derivatives are used in a variety of scientific and mathematical applications, such as modeling physical systems, optimizing functions, and solving differential equations. They also have practical applications in fields such as economics and finance.

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

The derivative of a function can be found using various techniques, such as the power rule, product rule, and chain rule. It involves differentiating the function with respect to its independent variable and simplifying the resulting expression.

4. What is the relationship between derivatives and graphs?

The derivative of a function represents the slope of its graph at a specific point. This means that the derivative can be used to determine the steepness or direction of a curve at a given point.

5. Can derivatives be negative?

Yes, derivatives can be negative. This indicates that the function is decreasing at that point, meaning its output is decreasing as its input increases. A positive derivative indicates that the function is increasing at that point.

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