I need help solving this derivative using the chain rule. I have tried setting $u = -x^2$

There is black semicircle, which radius is $ R $. The red circle is tangentially inward to the semicircle and to the diameter in its center. The yellow on...

I have a circle who center $(0, 0)$ and radius $100$ are known. That circle is divided into $6$ equal parts. I want to know the coordinates of all six poi...

In finite geometry, the Fano plane is the finite projective plane with the smallest possible number of points and lines: 7 each. Why its automorphism grou...

How do mathematicians pronounce "Hessian"? From searching online I've learned that the term is named after Otto Hesse, a German, and that the German ...

I'm reading a Wikipedia article about equality and its axioms and I'm wondering how we can prove (using equality axioms) that: If $x = y$ then $...

I have an operator $\hat{L}$ which gives $$\hat{L} f(x) = \lambda \cdot f(x)$$ where $\lambda$ is the eigenvalue. Now I Fourier-Transform my function $f(x...

I am doing a project in stochastic differential geometry mainly(Brownian motion on manifolds) ,the proof of laplacian-beltrami operator. I am currently re...

I want to read about famous Indian mathematicians (for example, Ramanujan, Aryabhatta, etc.), their biographies and their research contributions. Please s...

I'm wondering what is the difference in the use of $$\lim\limits_{x \downarrow a}$$ $$\lim\limits_{x \searrow a}$$ $$\lim\limits_{x \nearrow a}$$ $$\...