Haseo21 said:
I 'll cut to the chase
I need to know how to write a vector expression for x & y ( lets say that x and y are functions of time) using unit vectors.
I need to know how to take the derivative of said function ( I dont know if there is some special way you do it if your using unit vectors, I know how to take derivatives of normal functions)
Any help is much appreciated.
A little more information might be helpful. What is the unit vector describing? Displacement? Velocity? Acceleration? I am assuming you already have an equation to describe displacement/velocity/acceleration and that it just needs to be translated into a unit vector. I am trying to think, it has been a few years, it might be helpful to provide a more specific example. It can get tricky since the magnitude and direction of the vector would be constantly changing with time.
In regards to the derivative function, it all depends on what variables are in the equation and what you are taking the derivative with respect to. The way derivatives work, any variables in the equation that are not part of the derivation are taken as constants. I would assume your equation(s) would be derived with respect to time (t). Here are a few examples that might help:
x = sin(t) + 5 ===> dx/dt = cos(t)
y = 4t^2 - 3t + 40 ===> dy/dt = 8t - 3
If you have multiple variables in a single equation, then you treat the other variables as constant, for example:
t = 5x - 3y + 10xy
dt/dx = 5 + 10y
dt/dy = -3 + 10x
I don't know if that is very clear, but hope that helps.
