How do you find the derivative of x/(1+x^2)x1+x2?

2 Answers
Jun 3, 2018

Use the rule (f/g)´=(f´·g-f·g´)/g^2

Explanation:

If y=x/(1+x^2)

Then

y´=(1·(1+x^2)-x·2x)/(1+x^2)^2=(1-x^2)/(1+x^2)^2

Where f=x and g=1+x^2

Jun 3, 2018

(1-x^2)/(1+x^2)^2

Explanation:

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

"given "f(x)=(g(x))/(h(x))" then"

f'(x)=(h(x)g'(x)-g(x)h'(x))/(h(x))^2larrcolor(blue)"quotient rule"

g(x)=xrArrg'(x)=1

h(x)=1+x^2rArrh'(x)=2x

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

=(1+x^2-2x^2)/(1+x^2)^2=(1-x^2)/(1+x^2)^2