Why $u = 1 + x^2 \implies du = 2x\ dx$?
27812
Understanding the differential $dx$ when doing $u$-substitution
115460
Proving $a\mid b^2,\,b^2\mid a^3,\,a^3\mid b^4,\ldots\implies a=b$ - why is my approach incorrect
122737
How to understand why $x^0 = 1$, where $x$ is any real number?
106305
Prove/disprove: if $\det(A+X) = \det(B + X)$ for all $X$, then $A=B$
14576
$(U\cap W)^0 = U^0 + W^0$
124121
Is this logic behind the derivative of $x^x$ a coincidence?
147207
Is it always true that $\det(A^2+B^2)\geq0$?
20532
Are these solutions of $2 = x^{x^{x^{\:\cdot^{\:\cdot^{\:\cdot}}}}}$ correct?
153794
What is the meaning of $1/(D+a)$, where $D$ is the derivative operator?
76589
When does product of derivatives equals derivative of products?
25730
Solve $u_x + u_y + u = e^{x+2y}$
97057
Show $a^2+b^2+c^2=1$ $\implies$ $ \dfrac {b^2c^2}{1+a^2} +\dfrac {c^2a^2}{1+b^2}+\dfrac {a^2b^2}{1+c^2} \le \dfrac 14 $
17928
How to prove the following expression does not depend on x?
2315
How to prove that $\lVert x + y\rVert = \lVert x\rVert + \lVert y \rVert \implies \lVert tx + (1-t)y\rVert = t\lVert x\rVert + (1-t)\lVert y \rVert$?
100845
How to prove that $G(x)=ax+b$ is a one-to-one correspondence where $a\neq0$ and $a,b\in\mathbb{R}$.
123911
Why is the derivative of a vector orthogonal to the vector itself?
158610
Why is the differentiation of $e^x$ is $e^x$?