How do you use the chain rule to differentiate #y=sqrt(x^2-7x)#?

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Answer 1 · 2017-05-10T13:01:13

#dy/dx=(2x-7)/(2sqrt(x^2-7))#

First, let #u=x^2-7x# and #y=sqrt(u)#

The chain rule uses the above manipulation in the following equation.

#dy/dx=(dy)/(du)(du)/(dx)#

Take the derivative of #u# and #y# respectively

#(dy)/(du)=d/(du)(sqrt(u))=1/(2sqrt(u))#

#(du)/(dx)=d/(dx)(x^2-7x)=2x-7#

Now multiply them, recalling that #u=x^2-7x#

#dy/dx=(dy)/(du)*(du)/(dx)#

#=1/(2sqrt(u))*(2x-7)#
#=(2x-7)/(2sqrt(x^2-7))#