Using the formal definition of the derivative, prove that the exponential function is its own derivative
102013
The derivative of $e^x$ using the definition of derivative as a limit and the definition $e^x = \lim_{n\to\infty}(1+x/n)^n$, without L'Hôpital's rule
105293
Proof of the second symmetric derivative
125615
Defining the derivative without limits
119907
Finding the Derivative of |x| using the Limit Definition
116832
Appearance of Formal Derivative in Algebra
51922
Epsilon Delta Proof: How do I use the definitions to prove
133917
$100$-th derivative of the function $f(x)=e^{x}\cos(x)$
57193
Prove that $f$ has derivatives of all orders at $x=0$, and that $f^{(n)}(0)=0$ for $n=1,2,3\ldots$
105767
derivative under integral intuition
88559
Which function (s) is(are) the k-th derivative of itself?
156536
Defining functions as derivatives
128998
Relation between real roots of a polynomial and real roots of its derivative
100780
Deriving upper bound for derivative of analytical function
79024
the derivation of E(X|X)
158610
Why is the differentiation of $e^x$ is $e^x$?
1641
Proving $f' = - \frac{\partial{F}/\partial{x}}{\partial{F}/\partial{y}}$
69008
$f'(x) = [f(x)]^{2}$. Prove $f(x) = 0 $