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# Basic Derivatives

### Basic Calculus Derivatives (with D standing for the differential operator)

D(a constant) 0
D[c f(x)] c f'(x)
D[f(x)+g(x)] f'(x) + g'(x)
D[f(x)- g(x)] f'(x)- g'(x)
D[f(x)g(x)] f(x)g'(x) + g(x)f'(x)
D[f(x)/g(x)] [g(x)f'(x)- f(x)g'(x)]/[g(x)]^2
D[f(g(x))] f'(g(x))g'(x)
D[x^n] nx^(n-1)
D[e^x] e^x
D[a^x] a^x ln a
D[ln x] 1/x
D[sin x] cos x
D[cos x] -sin x
D[tan x] sec^2 x
D[sec x] sec x tan x
D[csc x] -csc x cot x
D[cot x] -csc^2 x
D[arcsin x] 1/√(1-x^2)
D[arctan x] 1/(1+x^2)
D[arcsec x] 1/(x√(x^2-1))
Created by: jessicacraig