Potential Energy: Why Don't We Use Product Rule?

[matt_crouch]

Homework Statement

i wasnt really sure where to put this question. its kind of a maths question i suppose

the potential energy funtion u along the x-axis is given as

U=-U₀x²

the question is really why do i not use the product rule on this equation as it is two variable multiplied together

i am told that the answer is u₀2x
but I am a bit confused as to why you don't seem to do anythign with the first term apart from multiplied by -1 but still remains there. Is it to be treated as a constant? if so why does it not = 0 when differentiated.

any help would be appreciated =]

Homework Equations

The Attempt at a Solution

 

[Doc Al]

i am told that the answer is u₀2x
but I am a bit confused as to why you don't seem to do anythign with the first term apart from multiplied by -1 but still remains there. Is it to be treated as a constant? if so why does it not = 0 when differentiated.

I presume the question is to find the force given that potential function. In any case, U₀ is a constant. Go ahead and use the product rule if you like; the derivative of a constant is zero.

If y = ax², what's dy/dx? (a is a constant)

 

[matt_crouch]

sorry ye the question to find the force. and y=ax² will differentiate to 2x but i don't understand in the question the answer has the constant still in it after its be differentiated

:/

 

[matt_crouch]

aaahh wait i see if i differentiate it using the product rule i do get that answer..
i see why now

dy/dx= da/dx.x²+2x.a but because da/dx = 0 it removes the whole of the first term.

makes more sense now
cheers