Derivatives and integrals
Type a function of x, such as x³ − 2x or sin(x)·eˣ. The derivative comes back as a formula you can copy into the function plotter.
Result
- f''(x)
- 6x − 6
- f(1)
- 0
- f'(1)
- −3
- Tangent line
- y = −3x + 3
- f''(1)
- 0
The derivative is simplified automatically; sometimes it can be written more compactly.
How the derivative is found
The tool uses the same rules you learn in class: the sum rule, the product rule (u·v)' = u'v + uv', the quotient rule (u/v)' = (u'v − uv')/v², and the chain rule for composite functions. It knows the derivatives of trigonometric, exponential, logarithmic and root functions.
The derivative at a point is the slope of the tangent. The tangent at x₀ is y = f'(x₀)·(x − x₀) + f(x₀).
Definite integrals
The integral from a to b is the area under the curve, with parts below the x-axis counted as negative. It is calculated numerically with Simpson’s rule to about 10 digits, so it also works for functions with no closed-form integral, such as e^(−x²).
Common questions
How do I type eˣ or a square root?
e^x, √x or sqrt(x). You can skip the multiplication sign: 2x, 3sin(x). Angles are in radians.
Does it do indefinite integrals?
No, only definite ones (numerically). Derivatives are symbolic.