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| — | math [2025-12-14 Sun 02:19] (current) – theorytoe | ||
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| + | ====== Transform Tables ====== | ||
| + | * [[math: | ||
| + | * [[math: | ||
| + | * [[math: | ||
| + | |||
| + | ====== Useful Equations ====== | ||
| + | |||
| + | ^ Eulers Formula | ||
| + | ^ Eulers Cosine | ||
| + | ^ Eulers Sine | $$\sin(x) = \frac{je^{-jx}}{2} - \frac{je^{jx}}{2}$$ | | ||
| + | ^ Angular Frequency | $$\omega = 2\pi f$$ | | ||
| + | ^ Period | ||
| + | |||
| + | ====== Common Integrals ====== | ||
| + | |||
| + | | $$\int\, | ||
| + | | $$\int\, | ||
| + | | $$\int\, | ||
| + | | $$\int\, | ||
| + | | $$\int\, | ||
| + | | $$\int\, | ||
| + | |||
| + | ====== Common Derivatives ====== | ||
| + | |||
| + | | $$\frac{d}{dx}(f(x)g(x)) = f(x)\dot{g}(x) + \dot{f}(x)g(x)$$ | ||
| + | | $$\frac{d}{dx}\left(\frac{f(x)}{g(x)}\right) = \frac{f(x)\dot{g}(x)-\dot{f}(x)g(x)}{(g(x))^2}$$ | | ||
| + | | $$\frac{d}{dx}(\sin(x)) = \cos(x) $$ | | ||
| + | | $$\frac{d}{dx}(\cos(x)) = -\sin(x) $$ | | ||
| + | | $$\frac{d}{dx}(\tan(x)) = \sec^2(x) $$ | | ||
| + | | $$\frac{d}{dx}(\sin^{-1}(x)) = \frac{1}{\sqrt{1-x^2}}$$ | ||
| + | | $$\frac{d}{dx}(\cos^{-1}(x)) = \frac{-1}{\sqrt{1-x^2}}$$ | ||
| + | | $$\frac{d}{dx}(\tan^{-1}(x)) = \frac{1}{1+x^2}$$ | ||
| + | | $$\frac{d}{dx}(a^x) = a^x\ln(a)$$ | ||
| + | | $$\frac{d}{dx}(\ln|x|) = \frac{1}{x}$$ | ||
| + | | $$\frac{d}{dx}(\log_a(x)) = \frac{1}{x\ln(a)}$$ | ||
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