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