Derivatives & integrals
Formula tables and rules
| xⁿ | → n·xⁿ⁻¹ |
| eˣ | → eˣ |
| aˣ | → aˣ·ln a |
| ln x | → 1/x |
| sin x | → cos x |
| cos x | → −sin x |
| tan x | → 1/cos²x |
| √x | → 1/(2√x) |
| 1/x | → −1/x² |
| u·v | → u'v + uv' |
| u/v | → (u'v − uv')/v² |
| f(g(x)) | → f'(g)·g' |
Rules
- Derivative of sum = sum of derivatives
- Constants factor out: (c·f)' = c·f'
- Chain rule for composites
- Integral = antiderivative + C
- Substitution — reverse chain rule
- Integration by parts: ∫u dv = uv − ∫v du