1. ## two calculus problems

hey all i'm having alot of bother with these two questions. any comments would be very much appreciated!!!

1)
show that the derivative of

arctan(a + x/1 -ax) is independent of a and explain why

2)
use the substitution x-p = 1/u to show the integral of

1/(x-p)sqrt((x-p)(x-q)) = 2/(q-p) . sqrt((x-q)/(x-p))

thanks muchly!!!!!

2. First one:

First you note that $\frac d {dx} \left({\tan^{-1} z}\right) = \frac 1 {1 + z^2} \frac {dz}{dx}$ where $z = f \left({x}\right)$ where here $z = \frac {a + x}{1 - ax}$.

Yuch. The algebra's messy, but when you flog through it you'll find that $a$ does not appear in the final equation.

3. Originally Posted by laura90
hey all i'm having alot of bother with these two questions. any comments would be very much appreciated!!!

1)
show that the derivative of

arctan(a + x/1 -ax) is independent of a and explain why

2)
use the substitution x-p = 1/u to show the integral of

1/(x-p)sqrt((x-p)(x-q)) = 2/(q-p) . sqrt((x-q)/(x-p))

thanks muchly!!!!!
$\tan^{-1}\frac{a+x}{1-ax} = \tan^{-1} a + \tan^{-1} x + k\pi, k\in \mathbb{Z}$