^{2}. In this case the second term is zero so the answer will be y' = (dx/dx)/k

P=2RT/3b what is dp/dT? (differentiation) I know the answer is 2R/3b but can't see the steps to get there

Tutors, sign in to answer this question.

The derivative of a fraction is: y=x/k => y'= (k(dx/dx) - x(dk/dx))/k^{2}. In this case the second term is zero so the answer will be y' = (dx/dx)/k

P=2RT/3b

(dP/dT)= (2T)/3b

I do not see anything to any power.

Thanks

I don't see why the second term is zero though. I have included what I though was right in a comment to my original question.

I am not seeing the wood for the trees here I fear...

The second term of the derivative is Zero because b in this case is a constant and the derivative of a constant is equal tozero. I hope I explained and answered your question.

Ah, I think I may have seen a glimmer.

P=2RT/3b

let u=2RT let v = 3b

du/dx=2R** dv/dx=3**

let u=2RT let v = 3b

du/dx=2R

So, because b is a constant and (3 x b) is a constant, then in this case dv/dx = 0?

Is that reasoning correct?

Rearrange P=2RT/3b into the form

P = 2R/3b * T

This looks an awful lot like y = mx! If y = mx, then we know the curve is a line, and the derivative is the slope, dy/dx = m.

In your problem, P is y, T is x, and m is 2R/3b.

so dP/dT = 2R/3b!

This is simply done this way because R and B are not also functions of T.

Ethan G. | Engineering Grad for Math and Science TutoringEngineering Grad for Math and Science Tu...

So, another way to think about this problem is "What is the change of P with respect to change of T?" Since the only two variables we are looking at is P and T, R and b are constants, thus don't change, thus they can be "ignored".

So when you differentiate P with respect to T, remember

if F(x) = x^b, where b = exponent then...

So when you differentiate P with respect to T, remember

if F(x) = x^b, where b = exponent then...

dF(x) = x^b dx

= bx^(b-1)

So in this case, dP/dT ==>

dP = T dT where b = 1

= (1)T^(1-1)

= T^(0)

= 1

So dP/dT = 2R(1) / 3b

Already have an account? Log in

By signing up, I agree to Wyzant’s terms of use and privacy policy.

Or

To present the tutors that are the best fit for you, we’ll need your ZIP code.

Your Facebook email address is associated with a Wyzant tutor account. Please use a different email address to create a new student account.

Good news! It looks like you already have an account registered with the email address **you provided**.

It looks like this is your first time here. Welcome!

To present the tutors that are the best fit for you, we’ll need your ZIP code.

Please try again, our system had a problem processing your request.

## Comments

dF(x) = x^b dx

= x^(b-1) / b