Derivative Chain Rule Question

In summary, the conversation discusses the use of the chain rule to find the derivative of 2/x with respect to time. The correct answer is obtained by applying the chain rule and using the definition of time derivative of position as velocity.
  • #1
AirForceOne
49
0
Hi,

Say x=position, v=velocity, a=acceleration, t=time.

IyzKe.jpg


Thanks!

EDIT: I just realized that 2/x is not a constant and thus I shouldn't have treated it as a constant (taking the derivative of it as 0). However, I don't understand how to take the derivative with respect to t of it.
 
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  • #2
AirForceOne said:
Hi,

Say x=position, v=velocity, a=acceleration, t=time.

IyzKe.jpg


Thanks!

EDIT: I just realized that 2/x is not a constant and thus I shouldn't have treated it as a constant (taking the derivative of it as 0). However, I don't understand how to take the derivative with respect to t of it.

Use the chain rule.
d/dt(2/x) = d/dx(2/x) * dx/dt

If you work through this, you'll get what you show as the correct answer.
 
  • #3
By definition the time derivative of position is velocity.
 
  • #4
Ugh, I forgot how to use the chain rule *slaps forehead*. I get it now. It was hard to visualize 2/x as a "function within a function".

Thanks guys!
 

What is the derivative chain rule?

The derivative chain rule is a mathematical formula used to find the derivative of a function that is composed of two or more functions. It states that the derivative of a composite function is equal to the product of the derivative of the outer function and the derivative of the inner function.

How do I use the derivative chain rule?

To use the derivative chain rule, you first identify the outer function and the inner function of the composite function. Then, you take the derivative of the outer function and multiply it by the derivative of the inner function. It is important to use the chain rule whenever you encounter nested functions in a mathematical expression.

What are some common mistakes when using the derivative chain rule?

One common mistake when using the derivative chain rule is forgetting to apply the chain rule and instead using the power rule. Another mistake is not correctly identifying the inner and outer functions, which can lead to an incorrect derivative.

What is the purpose of the derivative chain rule?

The derivative chain rule is used to find the rate of change of a function with respect to its independent variable. It is an essential tool in calculus and is used in many real-world applications, such as physics, economics, and engineering.

Are there any alternative methods to finding derivatives?

Yes, there are other methods to find derivatives, such as the power rule, product rule, quotient rule, and chain rule. Each method is useful in different situations, and it is important to understand when to use each one. The derivative chain rule is particularly useful when dealing with nested functions.

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