Question

How do you differentiate `f(x)= (x^2+1) (x+2)^2 (x-3)^3` using the product rule?

Answer 1

take log

Explanation:

after taking log
`log(f(x)) = log(x^2 + 1) + 2log(x + 2) + 3log(x - 3)`
now differentiating
`1/f(x)*f^'(x) = 2x/(x^2 + 1) + 2/(x+2) + 3/(x-3)`
now take f(x) to the other side and place it value
hence `f^'(x)` can be found
hope u find it helpful :)