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Common Diff Rules
Common Differentiation rules useful for ap calc AB
| Prime | Derivative |
|---|---|
| (constant)' | 0 |
| (x)' | 1 |
| (f+g)' | f'+g' |
| (f-g)' | f'-g' |
| (f●g)' | f'●g+f●g' |
| (f/g)' | (f'●g-f●g')/g² |
| Chain Rule | f'(g(x))●g'(x) |
| Inverse Rule | 1/f'(f⁻¹(x)) |
| (√(x))' | 1/2√(x) |
| (1/x)' | -1/x² |
| (eˣ)' | eˣ |
| (aˣ)' | aˣ●ln(a) |
| (ln x)' | 1/x |
| (logₐx)' | 1/(x●ln a) |
| (sin x)' | cos x |
| (cos x)' | -sin x |
| (tan x)' | sec²x |
| (cot x)' | -csc²x |
| (sec x)' | sec x●tan x |
| (csc x)' | -csc x●cot x |
| (arctan)' | 1/(1+x²) |
| (arccot)' | -1/(1+x²) |
| (arcsin)' | 1/√(1-x²) |
| (arccos)' | -1/√(1-x²) |
| (arcsec)' | 1 / (|x|●√(x²-1)) |
| (arccsc)' | -1 / (|x|●√(x²-1)) |
| (constant●f)' | constant●f' |
| (xⁿ)' | n●x⁽ⁿ⁻¹⁾ |
Created by:
julio1234
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