How do you differentiate #f(x)=4/(x+1)^2 # using the chain rule?

1 Answer
Oct 30, 2016

Answer:

#f'(x)=-8/(x+1)^3#

Explanation:

Express #f(x)=4(x+1)^-2#

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

#color(orange)"Reminder " color(red)(bar(ul(|color(white)(2/2)color(black)(dy/dx=(dy)/(du)xx(du)/(dx))color(white)(2/2)|)))#

let #u=x+1rArr(du)/(dx)=1#

and #y=4u^-2rArr(dy)/(du)=-8u^-3#

substitute these values into #dy/dx# writing u in terms of x.

#dy/dx=-8u^-3 xx1=-8/(x+1)^3#