 In this video, we provide the solution to question number eight for practice exam number three for math 1210 And we're asked to find the slope of the tangent line of the function f of x equals secant of x at the point that x equals Pi force now remember that the slope of the tangent line is the derivative So what they're asking for is the derivative f prime? evaluated at the point pi force So that's what we're after so the first thing I'm going to do is going to compute the derivative Since my function f of x is secant of x I didn't remember that the derivative of secant is going to be secant times tangent and So we need to we need to then evaluate that at pi force so f prime of pi force We're going to end up with secant of pi force Times tangent of pi force by all means you can use a calculator to help you But if you don't remember or don't if you don't have the calculator Don't know these things off the top of your head. You could try and just switch it into signs and cosines That might be a little bit easier sign a pi force over Cosine squared of pi force and what this turns out to be pi force there Note that sine pi force and cosine of pi force are both the square root of two over two So you end up with I'm actually going to prefer to write this as one over the square root of two That's the same thing as root two over two and so you get you get these things twice in the bottom Notice that the one over square root of two will cancel out with the top bomb Basically the sine of pi force is equal to cosine pi force so you're left with the reciprocal of the reciprocal of the square root of two That simplifies just to be the square root of two in which case we then see that the correct answer is B