How do you differentiate #f(x)=ln((x-1)/(x^2+1))#?

1 Answer
Jim G. · mason m
Apr 9, 2017

#f'(x)=-(x-1)/(x^2+1)#

Explanation:

#"use the "color(blue)"law of logarithms" " to express" f(x)" as"#

#f(x)=ln(x-1)-ln(x^2+1)#

differentiate using the #color(blue)"chain rule"#

#• d/dx(ln(f(x)))=(f'(x))/(f(x))#

#rArrf'(x)=1/(x-1)-(2x)/(x^2+1)#

#color(white)(rArrf'(x))=(x^2+1-2x(x-1))/((x-1)(x^2+1))#

#color(white)(rArrf'(x))=-(x^2-2x+1)/((x-1)(x^2+1))#

#color(white)(rArrf'(x))=-(x-1)^2/((x-1)(x^2+1))#

#color(white)(rArrf'(x))=-(x-1)/(x^2+1)#

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