Unformatted text preview: zero
• The derivative of 3x = 3
• The derivative of 3x2 = 6x
• The derivative of 3x3 = 9x2
• If an exponent is negative, don’t forget to bring down the negative sign!
Ex. 3x -2 so dy/dx = -6x -3
Several rules of exponents you may have forgotten which may come in handy:
• x0 = 1
• x1 = x
• x -2 = 1/x2
• x1/2 = √x (square root of x)
3. PARTIAL DIFFERENTIATION
• The partial derivative, ∂Y/∂X, measures the marginal change in Y associated with a very
small change in X, holding constant all other influences
• This sounds scarier than it actually is. In a partial derivative, you treat all variables as constant
except the ones you are taking the derivative with respect to. We use this technique when you
have two unknown variables in an equation rather than one. The "∂" symbol means partial
derivative. We use that instead of a "d" which is the symbol used for a "total" derivative.
• Any partial derivatives you have to take will only use the power function rule, and no
exponents will be involved, so they are really easy. In this case, the partial derivative is
simply the number and sign in front of the variable you are interested in.
Example: Qd = 200 – 3P + 40Y – 6Px (this is demand function; we’ll use these in Ch. 3 & 5)
∂Qd/∂Px = -3 (Y and Px are assumed to be constants so their derivative is zero)
= +40 (P and Px are assumed to be constants so their derivative is zero)
(P and Y are assumed to be constants so their derivative is zero) 3...
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- Fall '10