Finding the Derivative of Arctan(x) for a Camera Tracking Problem

[aurdav]

<< edited by berkeman after thread merge >>

 

[aurdav]

1. if a=arctan(x/132), what is da/dx

 

[lurflurf]

So you do not know off hand, how about
using implict differentiation?
lets just do a=arctan(x*t) we will let t=1/132 later
a=arctan(x*t)
so
tan(a)=x*t
{[sec(a)]^2}[da/dx]=t
solve for [da/dx]
recall [sec(a)]^2=1+[tan(a)]^2

 

[HallsofIvy]

Please! If you have registered for this forum then you are expected to show some effort of your own. This looks to me like a staightforward, elementary, problem. I don't know what hints to give you because you haven't said where it is you are stuck! You are making it look like you accidently wandered into the wrong classroom and picked up the wrong homework!

Do you know the derivative of arctan(x) with respect to x or can you look it up in your textbook?

Do you know the derivative of x/132?

Do you know the chain rule?

 

[aurdav]

Please! If you have registered for this forum then you are expected to show some effort of your own. This looks to me like a staightforward, elementary, problem. I don't know what hints to give you because you haven't said where it is you are stuck! You are making it look like you accidently wandered into the wrong classroom and picked up the wrong homework! LOL

Do you know the derivative of arctan(x) with respect to x or can you look it up in your textbook? NO

Do you know the derivative of x/132? NO

Do you know the chain rule? not well

You are not far off. I am looking for a formula for the derivative of arctan(a) where arctan(a)=1x/132

It is not my homework but if I provided enough detail I would appreciate the info

The problem is. A camera mount 132ft up a pole is tracking a car traveling toward the pole at 264ft/sec. How fast is the angle of the camera change when the car is directly below? a half second later? So angle (a) , y=132ft and dx/dt=264ft/sec . da/dt=da/dx*dx/dt. I don't know how to find da/dx. tan(a)=x/132 and a=arctan(x/132). that is all I know