The Derivative of The Trigonometric Tangent

Based on what you just learned, try to see if you can figure out the derivative of

Give it a try, if you want. If not, follow the explanation below.

A long time ago, we defined the tangent as the ratio of the sine over the cosine:

You obviously see that we have two functions of x.
We can use the quotient rule!

See a familiar pattern? Split the fraction.

Similarly, you can substitute for The Pythagorean Identity :

You did it! Feels good, doesn't it?
To get into further topics, you need to learn something which, i won't lie, may be confusing at first.