00:01
So we have the function y equals cosich inverse of 3x, all raise to the fourth power.
00:09
And we want to find the derivative.
00:12
So we need to remember one thing that the derivative, d by dx, of inverse of cosich of x, is equal to the following.
00:26
We have 1, sorry, negative 1 over the absolute value of x.
00:36
Times the square root of x squared plus 1.
00:40
And this is good as long as x is not equal to 0.
00:44
So that's the condition.
00:46
So when we find our derivative here, we need to keep this in mind.
00:50
So let's start off first with the outside function, which is this fourth power.
00:55
So four is going to come out front.
00:57
And then we have inverse close each of 3x, decrease the power by 1, so we get power of three.
01:06
And now we have the chain rule.
01:08
So the chain rule says that we need to multiply by the derivative of the inside.
01:13
So derivative of the inside is the cosich inverse of three x.
01:18
So that's where this comes in handy, this formula over here.
01:22
So chain rule, we're going to take the derivative of cosich inverse of three x.
01:35
So let's focus on this part here.
01:38
So this derivative is equal to, let's use our formula...