A mathematical rule useful for finding the derivative or instantaneous rate of change of a function that involves the form y = x^n. If n = 0, then the rate of change is zero, since any number x raised to the zero power is 1. To find the derivative when n is some other number other than 0, simply pull down the exponent n, multiply the entire function by n, then subtract 1 from the exponent after you pull n down and multiply. Basically:

1) y = x^n

2) y' = nx^n-1 (y' means take the derivative of the function with respect to x, so use the simple power rule!)

Piece of cake! One of the most helpful rules in calculus, because if you didn't have the simple power rule, then you would have to use the general form for a derivative, which takes alot longer than the method above.

1) y = x^n

2) y' = nx^n-1 (y' means take the derivative of the function with respect to x, so use the simple power rule!)

Piece of cake! One of the most helpful rules in calculus, because if you didn't have the simple power rule, then you would have to use the general form for a derivative, which takes alot longer than the method above.

Try these out! Just take the derivative as described above!

y = 3x^(-2)

y'= -6/(x^3)

y = 12x^0

y'= 0

y = 3x^(1/2)

y'= (3/2)x^(-1/2) or 3/2 times 1/squareroot of x

y = 3x^(-2)

y'= -6/(x^3)

y = 12x^0

y'= 0

y = 3x^(1/2)

y'= (3/2)x^(-1/2) or 3/2 times 1/squareroot of x

by Adam Smith
April 20, 2005

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