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

1 Answer
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)