How can you determine the derivative or integral of dx in a given problem?

In summary, the conversation discusses the confusion and difficulties in understanding how to take the derivative and integral of "dx". The speaker suggests that dx can easily be integrated by simply multiplying it by 1. They also mention that taking the derivative of dx with respect to x does not make sense and suggest giving more context as the symbol "dx" is used in various places in mathematics.
  • #1
zmike
139
0
I am in the middle of a problem and I have to take the integral of "dx" This is very confusing, I would guess x or 1 but neither really makes sense to me. How would you take the derivative of something to form dx?, similarly how would you take the derivative of dx^2.

Aside from knowing that dx meaning a very small bit of something, I have no idea how one can take the derv. or integ. or it. It just doesn't make any sense.

Please Help

Thanks
 
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  • #2
dx = 1*dx... this can easily be integrated.
 
  • #3
explain how to take the dervative of dx with respect to x
 
  • #4
zmike said:
explain how to take the dervative of dx with respect to x

If you mean d(dx)/dx, that doesn't make any sense. If you mean dx/dx that's just d/dx(x). The derivative of the function f(x)=x.
 
  • #5
Maybe you could give a little more context. The symbol "dx" is used in various different places in mathematics.
For example, if you consider dx as a 1-form on the real line, then the indefinite integral is x+c for any c. See http://en.wikipedia.org/wiki/Exterior_derivative"
 
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What is the difference between an integral and a derivative?

An integral is the inverse operation of a derivative. It calculates the area under a curve while a derivative calculates the slope of a curve at a specific point.

Why are integrals and derivatives important in science?

Integrals and derivatives are important in science because they allow us to model and analyze complex systems and phenomena. They are used in fields such as physics, biology, economics, and engineering to understand and predict how systems change over time.

What is the purpose of the "dx" in an integral or derivative?

The "dx" in an integral or derivative represents the variable over which the operation is being performed. It indicates that the operation is being performed with respect to that variable.

How is the integral or derivative of a function calculated?

The integral or derivative of a function is calculated using specific rules and formulas, depending on the type of function. For example, the derivative of a polynomial function is found by using the power rule, while the integral of a trigonometric function is found by using trigonometric substitution.

Can integrals and derivatives be used in real-life applications?

Yes, integrals and derivatives have many real-life applications, such as calculating the velocity of a moving object, finding the area under a demand curve in economics, and determining the rate of change of a population in biology. These operations are essential in solving real-world problems and making predictions.

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