How do you find the derivative of #sqrt(2x-1#)?

1 Answer
Alan P.
Jun 2, 2015

#f(x) = sqrt(2x-1) = (2x-1)^(1/2)#

Let #g(x) = x^(1/2)# and #h(x) = 2x-1#

Then #f(x) = g(h(x))#

and

#(d f(x))/dx#

#color(white)("XXXXX")## = color(red)((dg(x))/(dh(x))*color(blue)((d h(x))/(dx)))#

#color(white)("XXXXX")##=color(red)(1/2(h(x))^-(1/2)) *color(blue)( 2)#

#color(white)("XXXXX")##= 1/sqrt(2x-1)#

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