 Let's briefly recap the main results of section 2.4 in active calculus on derivatives of other trigonometric functions. We had already seen previously that the derivative of the sine function is the cosine function, and that the derivative of the cosine function is minus sine. We can put these two facts together with the quotient rule and some basic trigonometric identities now to get the derivatives of the remaining four trigonometric functions. For the cotangent function, which is defined to be cotangent of x is cosine of x divided by sine x, we use the quotient rule and the fundamental trigonometric identity that says sine squared of x plus cosine squared of x equals 1 to get that the derivative of cotangent of x is equal to negative cosecant squared of x, whenever x is a value that does not cause undefined values in the cosecant function. Likewise, and through the same kind of derivation, we get the derivative of the tangent function equal to the derivative of tangent is secant squared x, whatever x is a value that doesn't cause undefined values in the secant function. Again, you can derive these rules yourself, and that's actually part of your preview activities now, using just the definitions of the tangent or cotangent, the derivative rules for sine and cosine, the quotient rule, and the fundamental trigonometric identity. However, once we've obtained these derivative rules for the trig functions, we don't need to re-derive them every time we wish to use them. It's just helpful to know where these rules come from. The derivatives of the other two trigonometric functions, the secant and cosecant functions, will be obtained in your classwork through activities, so we're not going to give away any spoilers here at this time, but we'll get those derivatives rules through more or less the same process as we did for tangent and cotangent. We use the definition of the trig function, then the quotient rule to get the derivative, and then use trig identities to simplify.