Why is the derivative different using Quotient Rule?

Question

So the title is a bit vague, let me clarify.

I was trying to find the derivative of $\frac {x}{cos(x)}$

I figured, to avoid using the quotient rule I will just write it as $x*sec(x)$ which is easy to figure out using the product rule. So I got: $xsec(x)tan(x)+sec(x)$. When trying the quotient rule I get: $\frac {xsin(x)+cos(x)}{cos^2(x)}$. What am I not getting here? Thanks in Advance!

Answer 1

They're the same expression. Look at this plot here on desmos and you will see that they have the same plot.

To show this multiply the $x\tan x \sec x + \sec x$ expression by $\frac{\cos^2 x}{\cos^2 x}$.

Answer 2

The answers are the same because $$\frac{x\sin(x)+\cos(x)}{\cos^2(x)}=x\frac{\sin(x)}{\cos(x)}\sec(x)+\frac{\cos}{\cos^2(x)}=x\tan(x)\sec(x)+\sec(x)$$