Differential calculus formulas list

\[ \frac{d}{dx} c = 0 \\~\\ \frac{d}{dx} x^n = nx^{n-1} \\~\\ \frac{d}{dx} \textnormal{sin}(x) = \textnormal{cos}(x) \\~\\ \frac{d}{dx} \textnormal{cos}(x) = -\textnormal{sin}(x) \\~\\ \frac{d}{dx} \textnormal{tan}(x) = \frac{1}{\textnormal{cos}^2(x)} = \textnormal{sec}^2(x) \\~\\ \frac{d}{dx} e^x = e^x \\~\\ \frac{d}{dx} a^n = \textnormal{log}(a) a^x \\~\\ \frac{d}{dx} \textnormal{log}(x) = \frac{1}{x} \\~\\ \frac{d}{dx} \textnormal{arcsin}(x) = \frac{1}{ \sqrt{1-x^2} } \\~\\ \frac{d}{dx} \textnormal{arccos}(x) = -\frac{1}{ \sqrt{1-x^2} } \\~\\ \frac{d}{dx} \textnormal{arctan}(x) = \frac{1}{ \sqrt{1+x^2} } \\~\\ (cf)' = cf' (f + g)' = f' + g' \\~\\ (f - g)' = f' - g' \\~\\ (f \cdot g)' = f'g + fg' \\~\\ \left(\frac{f}{g}\right)' = \frac{f'g - fg'}{g^2} \\~\\ \frac{d}{dx} (f(g(x))) = f'(g(x))g'(x) \]

Calculus formula

Formula