# Please see below If pq+5p=q+95 defines the demand curve of a firm, where p is price and q is quantity demanded.   Derive an expression for the rate of change in the price of the firm with respect to quantity.

You need to form the price function, hence you need to isolate the term containing p to the left side.

Notice  that you need to factor out p to the left side such that:

`p(q+5) = q+95`

You need to express p in terms of q, hence you need to...

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You need to form the price function, hence you need to isolate the term containing p to the left side.

Notice  that you need to factor out p to the left side such that:

`p(q+5) = q+95`

You need to express p in terms of q, hence you need to divide by q+5 both sides such that:

`p = (q+95)/(q+5)`

You need to find the rate of change of price with respect to quantity, hence you need to differentiate the price function with respect to q using the quotient rule such that:

`(dp)/(dq) = ((q+95)'*(q+5) - (q+95)*(q+5)')/((q+5)^2)`

`(dp)/(dq) = (q + 5 - q - 95)/((q+5)^2)`

`(dp)/(dq) = -90/((q+5)^2)`

Hence, evaluating the expression that expresses the rate of change of price with respect to quantity yields `(dp)/(dq) = -90/((q+5)^2).`

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