How to prove this?

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Answer 1 · 2018-03-11T11:48:13

See below.

Re-writing #sqrt(x^2+-a^2)# as #(x^2+-a^2)^(1/2)#

Using the Chain Rule:

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

Let: #u=(x^2+-a^2)#

#dy/dx(x^2+-a^2)^(1/2)=1/2(x^2+-a^2)^(-1/2)*2x+0#

#->(2x)/(2(x^2+-a^2)^(1/2))=x/(x^2+-a^2)^(1/2)=x/(sqrt(x^2+-a^2))#

The thing to remember here is:

#a^2# is a constant.

So:

#dy/dxa^n=0#