How do you differentiate #f(x)=1/(sqrt(x-3)# using the chain rule?

1 Answer
Guilherme N.
Jan 1, 2016

Chain rule states that #(dy)/(dx)=(dy)/(du)(du)/(dx)#.
We'll also need two power rules here.

Explanation:

  • #a^-n=1/a^n#

  • #a^(m/n)=root(n)(a^m)#

So, we can rewrite it as #f(x)=(x-3)^(-1/2)#

Renaming #u=x-3#, we get #f(x)=u^(-1/2)# and can now differentiate it.

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

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