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Answer 1 · 2017-01-28T17:22:54

Use the properties of logarithms to break into two terms and the differentiate each term.

#dy/dx = 1/(2x + 18) - 1/(2x - 18)#

#y = lnsqrt((x+9)/(x-9))#

Use #ln(sqrt(a)) = 1/2ln(a)#

#y = 1/2ln((x+9)/(x-9))#

Use #ln(a/b) = ln(a) - ln(b)#

#y = 1/2ln(x+9)- 1/2ln(x-9)#

#dy/dx = 1/(2(x+9))- 1/(2(x-9))#

#dy/dx = 1/(2x + 18) - 1/(2x - 18)#