How to prove $\dfrac{d}{dx}e^x=e^x$?
30181
Proving that $\lim\limits_{x \to 0}\frac{e^x-1}{x} = 1$
18201
Why isn't the derivative of $e^x$ equal to $xe^{(x-1)}$?
124581
Solving $x^2 - 1 = e^x$
41558
Prove that $\frac4{abcd} \geq \frac a b + \frac bc + \frac cd +\frac d a$
132957
Prove that the derivative of $x^w$ is $w x^{w-1}$ for real $w$
50038
Proving that $e^\pi=e^{-\pi}$
135731
Is there a way to show that $e^x=\lim_{n\to \infty }\left(1+\frac{x}{n}\right)^n$?
15262
Prove $\exists \xi, \eta \in (0,1)$, such that $f(\xi)+f'(\eta)=\xi+\eta$.
11557
How to prove $\det(e^A) = e^{\operatorname{tr}(A)}$?
20626
Prove that $x^y < y^x$
48824
Prove: $ \frac{1}{\sin 2x} + \frac{1}{\sin 4x } + \cdots + \frac{1 }{\sin 2^n x} = \cot x - \cot 2^n x $
79024
the derivation of E(X|X)
87613
Infinitely differentiable functions: how to prove that $e^\frac{1}{x^2-1}$ has derivative of any order?
87567
How to prove $1+x \leq e^x~\forall x \in \mathbb{R}?$
68854
Proving $\mathcal{F}\left(\frac{d^n}{dx^n} f(x)\right)=(ik)^n\mathcal{F}(f(x))$.
94469
How to prove that $|HK| = \dfrac{|H| \; |K|}{|H \cap K|}$?
52380
How to prove the function $e^x$ is continous for all real numbers