Why is the derivative of $e^x$ equal to $e^x$? And why the derivative of $a^x$ is equal to $ a^x\ln a$?
158610
Why is the differentiation of $e^x$ is $e^x$?
136185
How $a^{\log_b x} = x^{\log_b a}$?
53918
whats the proof for $\lim_{x → 0} [(a_1^x + a_2^x + .....+ a_n^x)/n]^{1/x} = (a_1.a_2....a_n)^{1/n}$
61144
Derivative of $x^{x^{\cdot^{\cdot}}}$?
152617
Differentiate $f(x)=x^TAx$
125774
Derivative of $a^x$ from first principles
87613
Infinitely differentiable functions: how to prove that $e^\frac{1}{x^2-1}$ has derivative of any order?
152111
Difference between differentiation and derivatives
124121
Is this logic behind the derivative of $x^x$ a coincidence?
69187
What's my confusion with the chain rule? (Differentiating $x^x$)
134871
Using definition of derivative to differentiate $f(x)= \sqrt{x}+1$
157087
Can anyone explain why $a^{b^c} = a^{(b^c)} \neq (a^b)^c = a^{(bc)}$
38636
A basic question about exponentiation: when is $a^{xy}=(a^x)^y$?
43956
Differentiating $f(x)^{g(x)}$
60321
Use the definition of derivative to prove $\lim_{x\to 0}\ln(x+1)/x =1$
109364
What exactly is the difference between a derivative and a total derivative?
4735
Proof for alternative definition of the derivative