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Basic Derivatives
Basic Calculus Derivatives (with D standing for the differential operator)
| Question | Answer |
|---|---|
| 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
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