Differentiating i= v/r (1-e^-Rt/L) to Find di/dt: Product Rule or Other Rule?

  • Thread starter Thepiman
  • Start date
In summary, the conversation discusses how to differentiate the formula i = v/r (1-e^-Rt/L) to get di/dt. It is suggested to use the product rule or to distribute the v/r term and derive the sum. It is also important to be consistent with variable usage, and the correct answer is di/dt= (R/L)e^-Rt/L.
  • #1
Thepiman
4
0

Homework Statement



i= v/r (1-e^-Rt/L)

How would i go about differentiating this formula to get di/dt? Would I use the product rule or another rule?

Homework Equations



i= v/r (1-e^-Rt/L)

The Attempt at a Solution



di/dt= ?
 
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  • #2
Open the parenthesis, then differentiate
 
  • #3
You have many options. You can use the product rule or distribute the ##v/r## inside the parenthesis and derive the sum. If you make no mistake, the answer will be the same.

Go ahead, start solving and tell us what you get.
 
  • #4
I got di/dt= R/L x e^-Rt/L

Using the chain rule.
 
  • #5
Thepiman said:
I got di/dt= R/L x e^-Rt/L

Using the chain rule.
What happened to ##v/r##?
 
  • #6
Does it not cancel out?
 
  • #7
Thepiman said:

Homework Statement



i= v/r (1-e^-Rt/L)

How would i go about differentiating this formula to get di/dt? Would I use the product rule or another rule?

Homework Equations



i= v/r (1-e^-Rt/L)

The Attempt at a Solution



di/dt= ?

Thepiman said:
Does it not cancel out?

Are r and R different variables? I suspect from what you wrote that they aren't. If you mean them to be the same, then be consistent by not mixing upper and lower case letters. That is, don't use r and R interchangeably.

Thepiman said:
I got di/dt= R/L x e^-Rt/L

You have i = (V/R)(1 - e^(-Rt/L)) = (V/R) - (V/R)e^(-Rt/L)
Now differentiate with respect to t. The answer you got above is incorrect.
 

Related to Differentiating i= v/r (1-e^-Rt/L) to Find di/dt: Product Rule or Other Rule?

What is differentiating?

Differentiating is a mathematical process used to find the rate of change of a function with respect to its independent variable. It is also known as finding the derivative of a function.

Why do we need to differentiate?

Differentiation is important in many fields of science, including physics, chemistry, and economics. It allows us to understand how variables change over time and make predictions based on that information.

What is the difference between differentiation and integration?

Differentiation and integration are inverse operations of each other. Differentiation is used to find the derivative of a function, while integration is used to find the antiderivative of a function. In simpler terms, differentiation is used to find the slope of a curve, while integration is used to find the area under a curve.

What are some common techniques used for differentiation?

Some common techniques for differentiation include the power rule, product rule, quotient rule, and chain rule. These rules allow us to differentiate functions that are composed of different operations, such as multiplication, division, and composition.

How is differentiation used in real-life applications?

Differentiation is used in real-life applications to solve problems related to rates of change, optimization, and curve fitting. It is also used to analyze data and make predictions in fields such as engineering, biology, and finance.

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