Simple Chain Rule Question

1. Mar 4, 2013

parents

1. The problem statement, all variables and given/known data

Use chain rule to find the derivative of f(x)= sin(x)/(1+x^2)

2. Relevant equations

Chain Rule (f(g(x)))'*g'(x)

3. The attempt at a solution
y'(x)= cos (x)/(1+x^2)* (1-x^2)/((1+x^2)^2)

I just want to make sure I am doing it correctly and this would be acceptable as a final answer.

2. Mar 4, 2013

SammyS

Staff Emeritus
Hello parents. Welcome to PF !

Is the function $\ \displaystyle f(x)=\frac{\sin(x)}{1+x^2} \,,$

or is it $\ \displaystyle f(x)=\sin\left(\frac{x}{1+x^2}\right) \ ?$

3. Mar 4, 2013

parents

Sorry! I see how that can be confusing. It's $\ \displaystyle f(x)=\sin\left(\frac{x}{1+x^2}\right)$

I am working on trying to put in equations correctly

4. Mar 4, 2013

iRaid

Make the equation f(u)=sin(u). Then take the derivative of sin(u) then multiply by the derivative of u.

So:
f'(u)=sin(u)'u'

Last edited: Mar 4, 2013
5. Mar 4, 2013