Rate of change for R = R0(1+at+bt^2)^-1

[theinfinitemindfieled]

Hello,

Would like some help with this problem.

(1) The following formulae have been proposed to express the relation between the electric resistance R of a wire at the temperature t0C., and the resistence R0 of that same wire at 0 Centigrade, a, b, c are constants.

R = R0(1+at+bt^2)^-1

What I got was:
udv + vdu

R0(a+2bt) + -1R(1+at+bt^2)^-2

The book says the actual answer is:

-R0(a+2bt) / (1+at+bt^2)^2

or

R^2(a+2bt) / R0

Not really sure how the book got those answers.

Any help would be appreciated. Thanks

 

[Deleted member 4993]

Hello,

Would like some help with this problem.

(1) The following formulae have been proposed to express the relation between the electric resistance R of a wire at the temperature t0C., and the resistence R₀ of that same wire at 0 Centigrade, a, b, c are constants.

R = R₀(1+at+bt^2)^-1

What I got was:
udv + vdu

R0(a+2bt) + -1R(1+at+bt^2)^-2

The book says the actual answer is:

-R0(a+2bt) / (1+at+bt^2)^2

or

R^2(a+2bt) / R0

Not really sure how the book got those answers.

Any help would be appreciated. Thanks

In this case, you have:

R₀ = constant

So "product rule" is not pertinent here!

If you have y = A * x^-1 ......... (where A is a constant):

Do you know how to calculate dy/dx?