00:01
Here we're given some equations and we want to take the derivative.
00:04
So the key here is to know what rule to use.
00:07
So the first one, we just have the sine of stuff.
00:09
Well, the derivative of the sine of anything is the cosine of that stuff.
00:12
So this is going to be 5 times the cosine of x cubed minus x.
00:18
But then whenever you take any other rule, it doesn't matter which one it is, including the sine rule, you need to multiply by the derivative of the inside, which that's the chain rule.
00:25
So in this case, this is going to be the derivative of x cubed minus x, which is a power rule.
00:29
That's 3x squared minus 1.
00:32
We could distribute the 5 or whatever, but we don't really need to simplify.
00:36
For the next one, we have tangent.
00:38
The derivative of tangent is secant squared.
00:40
So we have 4 secant squared of the stuff, square root of x minus 1.
00:45
And just like before, we have to multiply then by the derivative of the inside for the chain rule.
00:50
So that's an x minus 1 to the 1 half.
00:52
So i'm going to multiply by a 1 half of x minus 1 to the negative 1 half.
00:57
Half...