Is it legal to use the product rule for finding the derivative of this? (in terms of x)

Question

chupacabraj · Answer

attachment

chupacabraj · Answer

My friend says that since it's a product he takes the derivative and ends up with -kx

chupacabraj · Answer

(-kx)

chupacabraj · Answer

Like i don't think it's necessary to do that, k is just a constant

chupacabraj · Answer

attachment

chupacabraj · Answer

Why is it negative???

chupacabraj · Answer

I got the answer wrong since I simply took the derivative. I got kx. don't know why it's negative.

chupacabraj · Answer

@IrishBoy123 why you left? :(

irishboy123 · Answer

why is it negative?!?!

irishboy123 · Answer

why should it be negative?!?!  you have it down to math.

irishboy123 · Answer

$ U =   \dfrac{1}{2} k x^2 $

$ \dfrac{dU}{dk} =   \dfrac{1}{2}  x^2 $

Nuts, isn't it !!!!!

chupacabraj · Answer

Yes

chupacabraj · Answer

But derivative of U with respect to x

chupacabraj · Answer

kx

chupacabraj · Answer

I guess, F=-dU/dx is just the definition of Force

it's the NEGATIVE derivative of energy

chupacabraj · Answer

It's just that my classmate confused me when he said that it was negative because of the freaking product rule. It didn't make sense to me but he just seemed so confident.