# Differentiation of tan^-1

1. May 28, 2007

### ahoy hoy

1. The problem statement, all variables and given/known data
f(x) = tan^-1[(10000-200x)/(26x^2-2750x+77725)
need to find f'(x)

2. Relevant equations

if f(x) = tan^-1 (x/a), then f'(x) = a/(a^2+ x^2)

3. The attempt at a solution

ok...the attempt im willing to do on my own, just needing help to get it in the form of x/a.
preciate it. thx.

Last edited: May 28, 2007
2. May 28, 2007

### matt grime

Why would you want to get it in that form? You know the chain rule, you know the derivative of tan^{-1}, and you can differentiate the expression inside your square brackets.

3. May 28, 2007

### Gib Z

Additional to what matt grime said, you need the quotient rule as well for the rational function that is the argument of the arctan.

4. May 28, 2007

### ahoy hoy

if f(x) = tan^-1[x/a], then f'(x) = [a/(a^2+x^2)]
thats the only way i can think of going about it.

5. May 29, 2007

### danago

$$f(x)=tan^{-1}(x)$$
$$f'(x)=\frac{1}{1+x^2}$$

With that, you can easily do it with the chain rule.

6. May 29, 2007

### ahoy hoy

will do. thanks. = )

7. May 30, 2007

### NateTG

As an aside the following identity is occasionally handy:
$$\frac{x}{1}=x$$
And brings your formula into line with danago's.

8. Jun 3, 2007

### HallsofIvy

Staff Emeritus
What?? We have to memorize complicated identities like that??