Derivatives of Roots

Example:

y = sqrt(x)

To take the derivative of any function involving a root, we notice that it's the same as a power function with a fractional exponent, and then use the power rule. Here,

^{1/ 2}

The Power Rule (Derivative Rule for Power Functions):

The derivative of any power function is the product of its exponent and a power function with the exponent decreased by one.
If

xⁿ

then the derivative of z is

z '

n x^n-1

So our example,

^{1/ 2}

Must have as its derivative

y '	=	1/ 2	x	^{1/ 2 - 1}
	=	(1/2)*x^-1/2

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Comments to Gavin LaRose
glarose@umich.edu
©2001 Gavin LaRose, University of Michigan Math Dept.