How do you find the derivative of #f(x) = 1/sqrtx#?

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Answer 1 · 2016-06-17T18:33:05

#y = 1/u^(1/2) = u^(-1/2)#

#u = x#

The chain rule states that #dy/dx = dy/(du) xx (du)/dx#. We must therefore we must differentiate both #u# and #y#.

#u' = 1#

#:.y' = -1/2u^(-3/2)#

#y' = -1/(2sqrt(u^3))#

#dy/dx = 1 xx -1/(2sqrt(u^3))#

#dy/dx = -1/(2sqrt(x^3))#

Hopefully this helps!