Proof of the derivative of $a^x$
125774
Derivative of $a^x$ from first principles
105293
Proof of the second symmetric 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
39451
Proving inequation with maximum and 2nd derivative
128998
Relation between real roots of a polynomial and real roots of its derivative
28297
derivative of x^x^x... to infinity?
60321
Use the definition of derivative to prove $\lim_{x\to 0}\ln(x+1)/x =1$
62067
Inverse function of $x^x$
73073
Differentiating $y=x^{2}$
75548
second derivative of the inverse function
156597
Proving a reduction formula for the antiderivative of $\cos^n(x)$
70304
Prove there are $\xi$, $\eta$ with $f'(\xi)f'(\eta)=1$
55018
Prove that $A^*A + I$ is invertible
43956
Differentiating $f(x)^{g(x)}$
157918
Finding the derivative of $x^x$
139288
Formal proof that $e^x$ is not algebraic
21553
Prove that $\nabla_{\mathrm X} \mbox{tr} (\mathrm A \mathrm X^{-1} \mathrm B) = - \mathrm X^{-\top} \mathrm A^\top \mathrm B^\top \mathrm X^{-\top}$