00:01
Okay, given this function f of x is secan of x over 1 plus tangent of x.
00:04
What i want to do is i want to find the first derivative.
00:07
And first thing i notice is that i have some trick functions here.
00:09
I have secant and tangent of x.
00:11
So it's just helpful to know what the derivatives of these trick functions are.
00:16
The derivative of secant is secan of x times tangent of x.
00:21
And then it's also helpful to note the derivative of tangent is secant squared of x.
00:28
Okay.
00:30
So just helpful to know as we're perceiving.
00:33
And when finding the first derivative, notice that i have two functions here.
00:36
I have sikin of x on top and one plus tangent of x on bottom.
00:40
So since i'm dividing two functions, what i'm going to do when i take the first derivative is i'm going to use the quotient rule.
00:46
So applying the quotient rule here, i'm going to do the derivative of the top function.
00:52
So the derivative of sikin of x is just sikin of x times tangent of x times the entire bottom function, 1 plus tangent of x, minus the top function, which is just sicken of x, times the derivative of the bottom function.
01:10
So the derivative of one, any constant, is just zero, plus the derivative of tangent is sqn squared.
01:16
So times sikin squared of x.
01:19
Okay, that's the numerator.
01:21
And then all over what the bottom term is, one plus tangent of x, that entire term raised to the second power...