Differentiate (Using Product Rule) (1 Viewer)

[Smile12345]

How do you differentiate this using the Product Rule?

4x(3x - 2)^5

I got 4(1 + 5x^2 -10x)(3x - 2)^4... I don't know what I've done wrong...

Thanks heaps.

 

[asianese]

 

[Smile12345]

I got the same for the 2nd line but then...

I got 4(3x-2)^5 + 20x(3x-2)^4
Then (3x-2)^4 [4 + 20x(x-2) ]
Then expanding and factorising the second brackets: 4(1+5x^2 -10x)(3x-2)^4

Thanks for your help...

 

[HeroicPandas]

I got the same for the 2nd line but then...

I got 4(3x-2)^5 + 20x(3x-2)^4
Then (3x-2)^4 [4 + 20x(x-2) ]
Then expanding and factorising the second brackets: 4(1+5x^2 -10x)(3x-2)^4

Thanks for your help...

Asianese perfectly differentiated it,

maybe u did a multiplication error

y = (3x-2)^5

dy/dx = 5 . 3 (3x-2)^4

dy/dx = 15(3x - 2)^4

 

[Smile12345]

Asianese perfectly differentiated it,

maybe u did a multiplication error

y = (3x-2)^5

dy/dx = 5 . 3 (3x-2)^4

dy/dx = 15(3x - 2)^4

Thanks for your help... Just wondering where the 4x went from the 2nd line?

 

[HeroicPandas]

Thanks for your help... Just wondering where the 4x went from the 2nd line?

There is no problem with 4x

I wanted to show u that u made a multiplication error while differentiating this particular term so i neglected the 4x

unless ur talking about Asianese's working,

he just used product rule

I dont clearly see ur problem with this....

 

[Smile12345]

There is no problem with 4x

I wanted to show u that u made a multiplication error while differentiating this particular term so i neglected the 4x

unless ur talking about Asianese's working,

he just used product rule

I dont clearly see ur problem with this....

Awe yeah, thanks... Yes, I realised it was the product rule (that's what I'm meant to be using)

Sorry, just a 'blonde' moment! (I'm not blonde!)

 

[asianese]

Asianese perfectly differentiated it,

That's flattering.

 

[HeroicPandas]

Awe yeah, thanks... Yes, I realised it was the product rule (that's what I'm meant to be using)

Sorry, just a 'blonde' moment! (I'm not blonde!)

Product rules is used when u have a product of 2 functions

eg. xe^x

Here is a very good question:

Given that y = (x)(x^2 )

Using product rule or otherwise, find dy/dx

 

[HeroicPandas]

That's flattering.

haha

 

[Smile12345]

Product rules is used when u have a product of 2 functions

eg. xe^x

Here is a very good question:

Given that y = (x)(x^2 )

Using product rule or otherwise, find dy/dx

Which is 3x^2... Am I correct here 'HeriocPandas'?

 

[Smile12345]

Thanks Asianese... Sorry to go back to this question, just writing it down now... In the 2nd line of working, how did you get x 3 in the first set of brackets? I thought it would have been without x 3)... I think I'm missing a basic here am I?

Thanks for your continued help as well HeriocPandas ...

 

[nightowl]

Thanks Asianese... Sorry to go back to this question, just writing it down now... In the 2nd line of working, how did you get x 3 in the first set of brackets? I thought it would have been without x 3)... I think I'm missing a basic here am I?

Thanks for your continued help as well HeriocPandas ...

If you just focus on



for a moment..

This is a (simple) example of the chain rule. The 3 is the derivative of 3x-2.

 

[HeroicPandas]

Which is 3x^2... Am I correct here 'HeriocPandas'?

Yes, I just hope that u didnt use product rule

 

[Smile12345]

Yes, I just hope that u didnt use product rule

Did you want me to?!

 

[Smile12345]

If you just focus on



for a moment..

This is a (simple) example of the chain rule. The 3 is the derivative of 3x-2.

Yes it is, so I need to add this in??

I appreciate any help...

 

[asianese]

To differentiate a function of a function, we use the rule:



Here and so then

 

[Smile12345]

To differentiate a function of a function, we use the rule:



Here and so then

Yeah, I get it now... Thanks heaps for your patience.... So this step, using the chain rule has to be done first before we can use the product rule from then... Am I correct?

 

[asianese]

Well, depends how you see it. There's both a product, and a chain rule. Just be systematic about it and you should be fine.

 

[Smile12345]

Well, depends how you see it. There's both a product, and a chain rule. Just be systematic about it and you should be fine.

Yeah ok. Thanks for you advice, I reckon I should be too... I will continue to practice with the questions after this one!