Expert: Scotto - 12/2/2008

Question
i just wanted to know that what is derivative?i'm mba student,i have to deal with derivatives in Demand function.The following are few exapmples of derivatives..can you please explain.it would be helpful to me...1)P(Price)=90,Q(quantity)=40,TR(Total Revenue)=P*Q=3600,MR(marginal Revenue)=dTR/dQ=80.How MR=80????How it came?
2)P=100-0.25Q,or Q=400-4P,ep(Point elasticity)=dQ/dP=-4.How dQ/dP=-4????????Please explain the method.

Answer
I don't know how the equations fit, but I can say that derivatives are not that hard when speaking of powers of x.

The derivative of x^n is nx^(n-1).  Basically, to take a derivative of each term, multiply each term by the exponet and reduce the exponet by 1.  If the exponet is one, then the variable disappears.  

Examples:

If f(x) = 4x, f'(x) = 4;

if f(x) = 7x, f'(x) = 7;

if f(x) = 7x + 17, f'(x) = 7;

if f(x) = 3x², f'(x) = 2*3x = 6x;

if f(x) = 5x^3, f'(x) = 3*5x² = 15x².

In the term dQ/dP, Q is being differentiated with P as the variable.  This means that all terms besides P are treated as constants.  dTR/dQ means to take the derivative of TR with Q as the variable.

In business, derivatives can be thought of as how much the next unit will sell for given the number of current sales.

1. Here, this means that if Q were increased by 1, TR would be increased by 80.

2. Here, Q = 400 - 4P, so dQ/dP is the derviatve of Q with respect to P, so it is -4 since this is the coeffient in front of P.

I hope this does it for you.