Derivative of tan(x)

In this video, we find the derivative of tan(x) by considering it as the quotient of sin(x)/cos(x). To find this derivative, we can use a method called the Quotient Rule, which is given by:

y' = \frac{vu'-uv'}{v^2}

So if we let:

u = sin(x)
v = cos(x)

Then...

u' = du/dx = cos(x)
v' = dv/dx = -sin(x)

And substituting these derivatives into the Quotient Rule, we get...

y' = \frac{\cos x\cdot \cos x-\sin x\cdot -\sin x}{\cos^2x}