Calculator
Supported: + − × ÷ ^, parentheses, sin cos tan asin acos atan sqrt ln log exp abs, constants pi and e.
Example data table
| Function f(x) | First derivative f'(x) | Quick note |
|---|---|---|
| x^3 - 4*x | 3*x^2 - 4 | Polynomial rule |
| sin(x) | cos(x) | Trig rule (radians) |
| exp(x)*ln(x) | exp(x)*ln(x) + exp(x)/x | Product + chain rules |
| sqrt(x) | 1/(2*sqrt(x)) | Power as sqrt |
| 1/(1+x^2) | -2*x/(1+x^2)^2 | Quotient rule |
These are standard forms. Your input may simplify differently, but stays equivalent.
Formula used
The first derivative of a function is defined as the limit:
f'(x) = limh→0 ( f(x+h) − f(x) ) / h
To compute derivatives efficiently, the calculator applies common rules:
- Linearity: (u±v)' = u'±v'
- Product: (uv)' = u'v + uv'
- Quotient: (u/v)' = (u'v − uv') / v²
- Chain: (g(u))' = g'(u)·u'
- Power: (xⁿ)' = n·xⁿ⁻¹ (for constant n)
How to use this calculator
- Type your function using standard operators and parentheses.
- Select the variable you want to differentiate with respect to.
- Pick Symbolic for an exact form, or Numeric for verification.
- Optionally enter a point to evaluate f(x) and f'(x).
- Enable the range table to generate values and downloads.
Tip: If your function includes trig terms, inputs are interpreted in radians.