\(\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}\Bigl( {\color{DarkGoldenRod}\sin}(x) \Bigr) = {\color{DarkSlateBlue}\cos}(x) \)
\(\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}\Bigl( {\color{DarkSlateBlue}\cos}(x) \Bigr) = -{\color{DarkGoldenRod}\sin}(x) \)
\(\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}\Bigl( {\color{ForestGreen}\sec}(x) \Bigr) = {\color{ForestGreen}\sec}(x){\color{Firebrick}\tan}(x) \)
\(\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}\Bigl( {\color{DarkOliveGreen}\csc}(x) \Bigr) = -{\color{DarkOliveGreen}\csc}(x){\color{Maroon}\cot}(x) \)
\(\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}\Bigl( {\color{Firebrick}\tan}(x) \Bigr) = {\color{ForestGreen}\sec}^2(x) \)
\(\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}\Bigl( {\color{Maroon}\cot}(x) \Bigr) = -{\color{DarkOliveGreen}\csc}^2(x) \)
\(\displaystyle \lim\limits_{x \to \infty} \frac{{\color{DarkGoldenRod}\sin}(x)}{x} = 1 \)
\(\displaystyle \lim\limits_{x \to \infty} \frac{{\color{DarkSlateBlue}\cos}(x)-1}{x} = 0 \)
\(\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}\Bigl( \mathrm{e}^x \Bigr) = \mathrm{e}^x \)
\(\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}\Bigl( b^x \Bigr) = \ln(b)b^x \)
\(\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}\Bigl( \ln(x) \Bigr) = \frac{1}{x} \)
\(\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}\Bigl( \log_b(x) \Bigr) = \frac{1}{\ln(b)x} \)