Question

How do you differentiate `f(x)=(x^3+x)/(4x+1)` using the quotient rule?

Answer 1

`(8x^3 + 3x^2 +1)/(4x + 1)^2`

Explanation:

You differentiate a quotient as follow:

`(f(x)/g(x))'=(f'(x)g(x)-f(x)g'(x))/(g(x))^2`

So, for `f(x)=(x^3 +x)/(4x+1)`

`(f(x)/g(x))'=((3x^2 +1)(4x+1)-(x^3+x)(4))/(4x+1)^2= (12x^3 +3x^2 +4x +1- 4x^3 - 4x)/(4x + 1)^2 = (8x^3 + 3x^2 +1)/(4x + 1)^2`

Hope this helps and I hope I didn't make any mistake because it's kind of hard to see since I'm using my phone :)