How to derive 2π x sec^2 (π x^2)

[eddy2017]

Hello, I would appreciate very much your help with this. I don't realize what is the first step i should follow in solving this. please, help me.
I believe a product rule that i have to derive first, and then a chain rule.
what do you think?
Thanks a lot,
Eddy

 

[Steven G]

I would use the rule that says that the derivative of kf(x) = k f'(x) for any constant k.
I would never use the product rule for 7(x+3)^2, for example.
If you do not understand how to use this in your problem then please ask.

 

[pka]

\(\displaystyle \tfrac{d}{dx}\left((2\pi x)(\sec^2(\pi x^2)\right)\)=\(\displaystyle \left(\tfrac{d}{dx}(2\pi x)\right)(\sec^2(\pi x^2)+(2\pi x)\left(\tfrac{d}{dx}(\sec^2(\pi x^2)\right)\tfrac{d}{dx}\left(\pi x^2\right)\)

 

[Steven G]

I thought that X was the student using a times symbol. Into the corner.

 

[pka]

I thought that X was the student using a times symbol. Into the corner.

That may well be the case. However not that there are two x's exactly the same type.
That seems odd if they are used in two different ways?

 

[eddy2017]

Thanks a lot to you all for your time and explanation. This question helped my daughter a lot. My questions are mostly about word problems which I struggle with.
Thank you once again.
I'm proud to post questions on this forum and its because of you all.