What is the derivative of #sqrt(2x-1)#?

1 Answer
Ken C.
Feb 3, 2016

#1/(sqrt(2x-1))#

Explanation:

This is a case of using the power rule and the chain rule.

First, we note that #sqrt(2x-1)# can be rewritten as #(2x-1)^(1/2)#.
Now we can apply the power rule, where we multiply the function by the exponent then decrease the exponent by one:
#d/dx(2x-1)^(1/2)=(1/2)(2x-1)^(1/2-1)#
#=1/2(2x-1)^(-1/2)#

Then we apply the chain rule, which tells us to multiply this result by the derivative of the "inside" function. In our case, the "inside" function is #2x-1# (because it is inside the square root), and its derivative is simply #2#. Our final derivative now becomes:
#1/2(2x-1)^(-1/2)*2=(2x-1)^(-1/2)#

In radical form, this is #1/(sqrt(2x-1))#.

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