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)
]

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