Does the formula $(x^n)' = nx^{n-1}$ fail for some value of $n \in \mathbb{Z}$?
66145
>Prove that $\frac d {dx} x^n=nx^{n-1}$ for all $n \in \mathbb R$.
89758
Is there a formula for $(1+i)^n+(1-i)^n$?
36906
Prove that $x^n+x^{-n} \in \mathbf{N}$ if $x+\frac1x \in \mathbf{N}$
48211
When is $(a+b)^n \equiv a^n+b^n$?
15838
Induction Proof that $x^n-y^n=(x-y)(x^{n-1}+x^{n-2}y+\ldots+xy^{n-2}+y^{n-1})$
88973
How do you calculate this sum $\sum_{n=1}^\infty nx^n$?
87665
Proving $x^n - y^n = (x-y)(x^{n-1} + x^{n-2} y + ... + x y^{n-2} + y^{n-1})$
59911
Looking for help with a proof that n-th derivative of $e^\frac{-1}{x^2} = 0$ for $x=0$.
63356
Can $x^{n}-1$ be prime if $x$ is not a power of $2$ and $n$ is odd?
102138
Why does $\sqrt{x^2}$ seem to equal $x$ and not $|x|$ when you multiply the exponents?
155096
If $f(x)=x^{n-1}\log x$, then the $n$-th derivative of $f$ is equals?
108382
Prove $x^n-1$ is divisible by $x-1$ by induction
141799
Is $2^{|\mathbb{N}|} = |\mathbb{R}|$?
25471
Irreducibility of $x^n-x-1$ over $\mathbb Q$
107976
Find a closed formula for $\sum_{n=1}^\infty nx^{n-1}$
133755
Is true that $\sum_{k=1}^n\frac{[kx]}{k}\leq[nx]$, for every $x\in\mathbb{R}$ and for every $n\in\mathbb{Z}^+$?
30781
Why the representation in the form of $Z'X(X'X)^{-1}X'Z$ can not be simplified into $Z'Z$