you know @TedShifrin I was dreaming yesterday that I took a math course called super course that covered pretty much all of the courses that I took as undergrad so far in 3 month
if you are given a function $x^3+1$ and then they said that theres a tangent on that function, and its slope is 3. how can you find the point of the tangent?
i want to udnerstand this algebra more.. when you have $x^2 = 3$ I need to get rid of the squared x, what I can do is square root both sides, but that doesn't get me a correct answer?
For $3x^2 = 3$, you should divide both sides by $3$ first, to get $x^2 = 1$. Then there are only two $x$-values that you can square to get $1$, and they are $x = \pm 1$.
I haven't been on MSE too long, but are these types terribly uncommon? It's not exactly unsolicited, but their sole purpose is clearly promotion of their website.
Let $y=Mx$ where $M$ is a matrix, not necessarily symmetric. I just calculated $\partial/\partial y=(M^{-1})^T\partial/\partial x$...but I've never noticed the transpose before. Can someone please tell me if that's correct?
@robjohn One more thing: I also realized that I can write a whole book starting from a single idea that is simply amazing.
I wonder how much one can go when starting from a simple idea. I guess the possibilities are very large, maybe countless, one only needs a bit of imagination.