How to Differentiate y=2e(2x+1) Using the Chain Rule?

In summary, the speaker is new to the forum and is asking for help with differentiating y=2e(2x+1) using the chain rule. They suggest letting u= (2x+1) and have already found that du/dx=2. They then ask for help with differentiating y=2eU and someone advises them to use the chain rule again, leading to the solution dy/dx=4e(2x+1). The speaker thanks everyone for their help and the conversation is moved to the Calculus and Analysis forum. The expert concludes that there is no need for a second application of the chain rule.
  • #1
v_pino
169
0
Hi everyone,

I'm new to this forum... I hope I've posted in the right section...

How do I differentiate y=2e(2x+1) using the chain rule?

I let u= (2x+1)

so du/dx = 2

but how do I differentiate y= 2eU ?

thank you :)
 
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  • #2
v_pino said:
how do I differentiate y= 2eU ?

thank you :)
Well, I see a multiplication and an exponentiation in that expression...
 
  • #3
Does it mean that I should use the chain rule again?

and I get dy/du = 2eU

so dy/dx = 4e(2x+1) ?
 
Last edited:
  • #4
The fact that a problem uses the word "differentiate" does not mean it is a differential equation! I am moving this to the Calculus and Analysis forum.
 
  • #5
First, do you mean
[tex]y= 2e^{2x+1}[/itex]
which in "ASCII" would be y= 2e^(2x+1). What you wrote, I would interpret as 2e times(2x+1) and there is no need for the chain rule!

If you let u= 2x+1, then, yes, the chain rule says that the derivative of y= 2e^u, with respect to x, is dy/dx= 2e^u (du/dx). Since you have already determined that du/dx= 2, that is dy/dx= 2e^(2x+1) (2)= 4 e^(2x+1). There is no need for a second application of the chain rule.
 
  • #6
thank you very much :)
 

FAQ: How to Differentiate y=2e(2x+1) Using the Chain Rule?

What is the chain rule and when is it used?

The chain rule is a mathematical concept used in calculus to find the derivative of composite functions. It is used when the function to be differentiated is made up of multiple functions nested within each other.

How do you differentiate using the chain rule?

To differentiate using the chain rule, you first identify the "outer" function and the "inner" function. Then, you take the derivative of the outer function and multiply it by the derivative of the inner function. This process is repeated if there are multiple nested functions.

Can you provide an example of differentiating using the chain rule?

Sure, let's say we have the function f(x) = (x^2 + 3x)^3. First, we identify the outer function as ( )^3 and the inner function as x^2 + 3x. Then, we take the derivative of the outer function, which is 3( )^2, and multiply it by the derivative of the inner function, which is 2x + 3. So the final derivative is 3(x^2 + 3x)^2 * (2x + 3).

Are there any common mistakes made when differentiating using the chain rule?

One common mistake is forgetting to take the derivative of the outer function. Another mistake is not using the chain rule when it is necessary, resulting in an incorrect derivative. It is also important to carefully apply the product and chain rules together, as they can be easily confused.

How does the chain rule relate to the power rule and product rule?

The chain rule is an extension of the power rule and product rule. It is used when the function to be differentiated is a composition of multiple functions, while the power rule and product rule are used for simpler functions. The chain rule can be thought of as a combination of the power rule and the product rule, as it involves both taking the derivative of the outer function and multiplying it by the derivative of the inner function.

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