Question

The demand x is the number of items that can be sold at a price of​ $p. For x equals p cubed minus 7 p squared plus 600 commax=p3−7p2+600, find the rate of change of p with respect to x by differentiating implicitly.

Answer 1

Answer:

1 ÷ [p(3p - 14)] = (dp/dx)

Explanation:

Given that,

Demand equation is as follows:

$x=p^{3}-7p^{2}+600$

where,

x is the number of items sold

$p is the selling price of the items

Now, differentiating the above equation with respect to 'x',

$1 = 3p^{2}\frac{dp}{dx} - 14p\frac{dp}{dx} + 0$

$1=\frac{dp}{dx}p(3p-14)$

1 ÷ [p(3p - 14)] = (dp/dx)

Therefore, the rate of change of p with respect to x by differentiating implicitly is 1 ÷ [p(3p - 14)] = (dp/dx)