How do you use the quotient rule to find the derivative of #y=x^3/(1+x^2)# ?

Question

2277 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2014-07-28T01:59:42

Answer ,

#y'=(3x^2+x^4)/(1+x^2)^2#

Explanation

Suppose,

#y=f(x)/g(x)#

Using Quotient Rule, which is

#y'=(f'(x)g(x)-f(x)g'(x))/(g(x))^2#

Similarly, following for problem

#y'=(3x^2(1+x^2)-x^3(2x))/(1+x^2)^2#

#y'=(3x^2+3x^4-2x^4)/(1+x^2)^2#

#y'=(3x^2+x^4)/(1+x^2)^2#