00:02
In this multiple choice question about the chain rule, we will be finding which of these five options is the derivative of tangent of 4x.
00:15
So let's use our knowledge of chain rule to find this.
00:22
We know that the derivative of a composite function is the derivative of the outside function at the inside function, multiplied by the derivative of the inside function.
00:35
In our case, we have the function 4x inside the tangent.
00:39
Function.
00:42
So first of all, what's the derivative of the outside, the tangent function? well, this is the well -known secant squared.
00:54
The derivative of tangent of theta is secant squared of theta.
01:01
So since we have tangent of this, its derivative is secant squared of that.
01:10
However, because of chain rule, we also need to multiply by the derivative of the inside function, which is this 4x.
01:19
The derivative of 4x is 4, which leads us to the conclusion that option e is correct...