How do you find the derivative of the function: #y = arctan(x - sqrt(1+x^2)#?

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Answer 1 · 2017-11-14T13:04:52

#y'=(sqrt(x^2+1)-x)/[sqrt(x^2+1)*(2x^2-2xsqrt(x^2+1)+2)]#

#y=Arctan[x-sqrt(x^2+1)]#

#tany=x-sqrt(x^2+1)#

#y'*(secy)^2=1-(2x)/[2sqrt(x^2+1)]#

#y'*[(tany)^2+1]=1-x/sqrt(x^2+1)#

#y'*([x-sqrt(x^2+1)]^2+1)=(sqrt(x^2+1)-x)/sqrt(x^2+1)#

#y'*(2x^2-2xsqrt(x^2+1)+2)=(sqrt(x^2+1)-x)/sqrt(x^2+1)#

#y'=(sqrt(x^2+1)-x)/[sqrt(x^2+1)*(2x^2-2xsqrt(x^2+1)+2)]#