00:01
Okay, so our goal here is to do implicit differentiation so we can find dr d theta.
00:07
Remember that r is a function of theta, so r kind of acts like your y, theta kind of acts like your x.
00:13
If you're used to doing implicit differentiation with x and y, feel free to replace them now and just go back and do that later, or just treat it like r is y and x is theta.
00:24
So, in order to do this, we're going to go ahead and take the derivative of both sides.
00:29
So on the left, the derivative of sign is going to be cosine.
00:42
And you can see that inside our sign.
00:45
We actually have two functions.
00:46
We have r times theta.
00:47
So this is going to be a chain rule since we have something on the inside there.
00:51
So we're going to need to multiply by the derivative of r theta.
00:56
And that itself is a product, r times theta, two different functions being multiplied together, two different things concerning r.
01:06
So we're going to do our product rule here.
01:09
Derivative of the first function, derivative of r.
01:11
That is just drd theta times the second function, theta, plus derivative of the second function, the derivative of theta is going to be one, again, just like x derivative, but x is one, times the second function, or times the first function...