Algebraic: d/dx(c) = 0, d/dx($x^n$) = nx^(n-1), d/dx(sqrt(x)) = $\frac{1}{2*sqrt(x}$)

Trigonometric: d/dx(sin x) = cos x d/dx(cos x) = -sin x d/dx(tan x) = $sec^2$ x d/dx(cot x) = -$cosec^2$ x d/dx(sec x) = sec x * tan x d/dx(cosec x) = -cosec x * cot x

Inverse Trigonometric: d/dx(sin^(-1) x) = 1/sqrt(1-$x^2$), |x| < 1 d/dx(cos^(-1) x) = -1/sqrt(1-$x^2$), |x| < 1 d/dx(tan^(-1) x) = $\frac{1}{1+x^2}$ d/dx(cot^(-1) x) = -$\frac{1}{1+x^2}$ d/dx(sec^(-1) x) = $\frac{1}{|x|*sqrt(x^2-1}$), |x| > 1 d/dx(cosec^(-1) x) = -$\frac{1}{|x|*sqrt(x^2-1}$), |x| > 1

Exponential & Logarithmic: d/dx($e^x$) = $e^x$ d/dx($a^x$) = $a^x$ * ln a (a > 0, a != 1) d/dx(ln x) = 1/x (x > 0) d/dx($log_a$ x) = $\frac{1}{x * ln a}$

Memory rule: All "co-" function derivatives carry a negative sign.