Derivatives elementary functions

It is possible to use the definition of the derivative to determine the derivative of a function. However, this is quite cumbersome. In Power functions and Exponential and logarithmic functions we discussed several elementary functions. Below we provide the derivative each of these elementary functions.
$$\begin{array}{c|ll|l} & y(x) && y'(x)\\ \hline (1) & c & & 0\\[2mm] (2) & x^k & & kx^{k-1}\\[2mm] (3) & a^x & (a>0) & a^x\ln(a)\\[2mm] (4) & e^x && e^x\\[2mm] (5) & ^{a\negthinspace}\log(x) & (a>0, a\neq1) & \dfrac{1}{x\ln(a)}\\[2mm] (6) & \ln(x) & & \dfrac{1}{x} \end{array}$$

Remark: Note that the derivatives of the functions $y(x)=e^x$ and $y(x)=\ln(x)$ follow directly from the derivatives of the exponential and logarithmic functions, respectively.