Differentiate; 3ln(x^2+1) ? Thanking the person(s) to help me in advance :)

2 Answers
Jun 13, 2018

(6x)/(x^2+1)6xx2+1

Explanation:

You need to know two major things for this:
1. Chain rule
2. The derivative of ln(x)ln(x) is 1/x1x
when you take the derivative you will get
3*1/(x^2+1)*31x2+1 the derivative of x^2+1x2+1 (because of chain rule)
so it's 3*1/(x^2+1)*2x31x2+12x
= (6x)/(x^2+1)6xx2+1

Jun 13, 2018

(6x)/(x^2+1)6xx2+1

Explanation:

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

"given "y=f(g(x))" then"given y=f(g(x)) then

dy/dx=f'(g(x))xxg'(x)larrcolor(blue)"chain rule"

d/dx(3ln(x^2+1))

=3xx1/(x^2+1)xxd/dx(x^2+1)

=3/(x^2+1)xx2x=(6x)/(x^2+1)