Derivate delle funzioni elementari
£$\textbf{(5.12)}$£$$\begin{array}{|c|cc|}\hline{\textbf{funzione}}&{\textbf{derivata}} \\ \hline{\text{costante}} &0 \\ \hline{x}& 1& \\\hline x^\alpha, \alpha\in\mathbb{R}&\alpha\cdot x^{\alpha-1}\\ \hline \sqrt x & \large\frac{1}{2\sqrt x}\\ \hline \sqrt[n]x, n\in \mathbb{N} & \large\frac{1}{n\sqrt[n]{x^{n-1}}} \\\hline \large\frac{1}{x} & -\large{\frac{1}{x^2}} \\\hline a^x,a > 0 & a^x\cdot \ln a \\\hline e^x & e^x \\\hline \text{log}_a x, \text{log}_a\mid x\mid & \large\frac{1}{x\cdot \ln a} \\\hline \ln x,\ln\mid x\mid &\large\frac{1}{x} \\\hline \text{sen }x &\cos x \\\hline \cos x &-\text{sen }x \\\hline \text{tg }x & \large\frac{1}{\cos^2x}\small{=1+\text{tg}^2x} \\\hline \text{cotg }x & -\large\frac{1}{\text{sen}^2x}\small{=-1-\text{cotg}^2x}\\\hline \text{arcsen }x & \large \frac{1}{\sqrt{1-x^2}}\\\hline \arccos x& -\large\frac{1}{\sqrt{1-x^2}} \\\hline \text{arctg }x & \large\frac{1}{1+x^2}\\\hline \text{senh }x & \cosh x \\\hline \cosh x & -\text{senh }x \\\hline\text{tgh }x & \large\frac{1}{\cosh^2x}\small =1-\text{tgh}^2x \\\hline \end{array}$$
