$$ \begin{array}{|c|c|} \hline y & \dfrac{dy}{dx} \\ \hline x^n & nx^{n-1} \\ \dfrac{1}{x} & -\dfrac{1}{x^2} \\ \sqrt{x} & \dfrac{1}{2\sqrt{x}} \\ a^x & a^x \ln a \\ e^x & e^x \\ \ln x & \dfrac{1}{x} \\ \hline \end{array} $$

$$ \begin{array}{|c|c|} \hline y & \dfrac{dy}{dx} \\ \hline \sin x & \cos x \\ \cos x & -\sin x \\ \tan x & \sec^2 x \\ \cot x & -\csc^2 x \\ \sec x & \sec x \tan x \\ \csc x & -\csc x \cot x \\ \hline \end{array} $$

$$ \begin{array}{|c|c|} \hline y & \dfrac{dy}{dx} \\ \hline \sin^{-1} x & \dfrac{1}{\sqrt{1 - x^2}} \\ \tan^{-1} x & \dfrac{1}{1 + x^2} \\ \sec^{-1} x & \dfrac{1}{x \sqrt{x^2 - 1}} \\ \hline \end{array} $$