How do you find the derivative of #sqrt(x^2+1)#?

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Answer 1 · 2015-08-16T01:33:51

This can be re-written to make it simpler. I hope you understand my method :)

You can re-write it as this:

#sqrt (x^2 + 1) # = #(x^2 + 1)^(1/2)#

After simplifying it, it is easy to apply the derivative rules.

#d/dx# = #(1/2)##(x^2 +1)^[(1/2) - 1]##*##2x#

# = # #1/2##(x^2 + 1)^(-1/2)# #*# #2x#

#=# #1/2 * # # 1/sqrt(x^2 +1)# #*# #2x#

# = # #(2x) / [2sqrt (x^2 +1)]#

#=# #x / sqrt(x^2 + 1)#