What is the derivative of #2 sqrtx# ?

1 Answer
Alan P.
Jun 7, 2015

In general if #f(x) = a*x^b#
#color(white)("XXXX")##(d f)/(dx) = b*a*x^(b-1)#

Since #f(x) = 2sqrt(x)#
is the same as #f(x) = 2*x^(1/2)#
#color(white)("XXXX")##color(white)("XXXX")##color(white)("XXXX")##(d f)/(dx) = (1/2) * 2 * x^(-1/2)#

#color(white)("XXXX")##color(white)("XXXX")##color(white)("XXXX")##color(white)("XXXX")##=1/sqrt(x)#

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