Algebraic: d/dx(c) = 0, d/dx(x^n) = nx^(n-1), d/dx(sqrt(x)) = 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) = 1/(1+x^2) d/dx(cot^(-1) x) = -1/(1+x^2) d/dx(sec^(-1) x) = 1/(|x|*sqrt(x^2-1)), |x| > 1 d/dx(cosec^(-1) x) = -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) = 1/(x * ln a)

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