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)