Okay, here we?re going to look at actually differentiating a function. Now, this shouldn?t be frightening because you already did this. You?ve done the differential of sin, cos, and tan. So anything after that is just going to be easy. Let?s have a look at the differential of cot of x and what we can do to differentiate it. So, we are finding the derivative d by dx of cot of x. Now, cot is a new identity for us. So, we don?t really know what the answer to this is yet but you can break it down. So, we can write this as d/dx and instead of using cot, why don?t we change it to 1 over tan x because we?re more familiar with that. So, using the identities at the start, we know that cot is 1 over tan and now we just have to differentiate 1 over tan x. A couple of ways of doing this but observe that I have a function at the top and a function at the bottom. Hopefully, this is ringing some bells. You have a function that is dividing a function, I have just called them u and v. So, hopefully, we?ll remember that we will have to use the quotient rule. Quotient rule, dy/dx is vdudx minus udvdx over v squared. In our case, our u is 1 and our v is tan x. When we differentiate u dashed, that?s zero, that?s always good news, and then when we differentiate tan we get sec squared x. Let?s apply the quotient rule now. So, we?re doing dy/dx, vdudx, so we?ll have tan of x multiplied by zero and then minus 1 times with sec squared of x over our v squared, so that?s going to be tan x all squared. We?re...
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