This is an extra example of how to find the derivative of the cotangent function, using power rule and chain rule.

We'll talk about the derivatives of each of the six trigonometric functions, how to apply chain rule when finding the derivatives of trig functions, and how to find the derivatives of higher-order trigonometric functions using power rule and chain rule.

If you need to use power rule to take the derivative of a function, but the inside function is not just x, you'll need to apply chain rule, multiplying the derivative of the power function by the derivative of the inside function.

Whenever you need to find the derivative of the product of two functions, you have to use product rule, you can't just take the derivative of each function separately and then multiply the results.

You can factor out the coefficient of a power function before using power rule to take the derivative. If you have the sum or difference of many power functions in the form of a polynomial function, you can use power rule on each term individually to find the derivative of the entire linear combination.

The definition of the derivative builds on the difference quotient and represents the slope of the tangent line.

The intermediate value theorem lets you prove that a function has a least one real root over a closed interval.

When you have a piecewise-defined function that includes a variable, you can find the value of that variable that makes the function continuous. Just plug in the value where the split occurs, then set the remaining two functions equal to one another and solve for the remaining variable. You're basically just finding the value that makes the left- and right-hand limits equal, which would make the function continuous.

If the graph of a function as a hole at a single point, it's called a removable discontinuity because the discontinuity can be removed just by redefining the value of the function at that singular point. Any rational function in which you can cancel the same factor from the numerator and denominator, has a removable discontinuity.

Functions are discontinuous where they are undefined, or where they have holes, breaks, gaps, corners, or jumps. When you define the domain of a function, you want to make sure to indicate that the function's points of discontinuity are not included the domain.