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

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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

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

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

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

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