How do I differentiate tan^-1[(10000-200x)/(26x^2-2750x+77725)]?

[ahoy hoy]

Homework Statement

f(x) = tan^-1[(10000-200x)/(26x^2-2750x+77725)
need to find f'(x)

Homework Equations

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

The Attempt at a Solution

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

 

[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.

 

[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.

 

[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.

 

[danago]

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

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

 

[ahoy hoy]

will do. thanks. = )

 

[NateTG]

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

 

[HallsofIvy]

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

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