Derivative calculator with steps
Enter a function and differentiate it. You see which rule applies where (power, constant, sum, product, quotient and chain rule), optionally the second derivative and the slope at a point. Every result is checked numerically before it is shown.
Result
- f(x)
- x²·sin(3x)
- f'(x)
- 2x·sin(3x) + 3x²·cos(3x)
Workings
- 1Product rule with u = x², v = sin(3x): (uv)' = u'v + uv'
- 2 ↳ Power rule: (x²)' = 2 × x = 2x
- 3 ↳ Chain rule with inner function u = 3x: outer derivative cos(3x) (sin' = cos), times inner derivative u'
- 4 ↳ u' = 3 → 3·cos(3x)
- 5 ↳ u' = 2x, v' = 3·cos(3x)
- 6→ 2x·sin(3x) + 3x²·cos(3x)
- 7Result: f'(x) = 2x·sin(3x) + 3x²·cos(3x)
The main rules
| Rule | Function | Derivative |
|---|---|---|
| Power rule | xⁿ | n·xⁿ⁻¹ |
| Product rule | u·v | u'·v + u·v' |
| Quotient rule | u / v | (u'·v − u·v') / v² |
| Chain rule | f(g(x)) | f'(g(x))·g'(x) |
Frequently asked questions
Why does my answer look different?+
Derivatives can be written in several equivalent ways, e.g. 2x(x + 1) or 2x² + 2x. Both are right if they are the same function.