# Differentiation: Given lnP= -X/RT + c,where X and R are constant..Compute dlnp/dT

### 2 Answers | Add Yours

You need to differentiate both sides such that:

`d(lnP)= (-X/RT)dT + c`

Notice that you need to differentiate the right side with respect to T, considering X,R and c as constants such that:

`d(lnP) = (-(X/R)*(T^(-1)) + c)(dT)`

`d(lnP) = ((-(X/R)*(-T^(-2)) + 0)dT`

You need to divide both sides by `dT` such that:

`(d(lnP))/(dT) = (X/R)*(1/(T^2))`

`(d(lnP))/(dT) = X/(RT^2)`

**Hence, evaluating `(d(lnP))/(dT)` under given conditions yields `(d(lnP))/(dT) = X/(RT^2).` **

**Sources:**

lnP = -X/(RT)+c

**if c is a constant**

d(lnP)/dT = -(X/R)d(1/T)/dT+d(c)/dT

= -(X/R)(-1/T^2)+0

= X/(RT^2)

so **d(lnP)/dT = X/(RT^2)**