Derivatives and Integrals, Fast
This mirrors what nDeriv and fnInt do on a physical TI-84 — compute a derivative or an integral instantly, without needing the device itself. Good for checking your own work, poking at how a function behaves at a specific point, or building intuition for AP Calc AB/BC or an intro college course.
What It Computes
- Derivatives: a function's instantaneous rate of change at a point, or the general derivative expression.
- Definite integrals: the signed area under a curve between two bounds.
- Indefinite integrals: the general antiderivative.
- Numerical approximations: for anything that doesn't have a clean closed-form answer.
Derivatives and Integrals, Quickly
A derivative tells you how fast a function is changing at a given instant — its slope right there. That's how you get velocity out of a position function, or find a maximum/minimum. A definite integral gives you the accumulated area under a curve between two x-values — how you get total distance from a velocity function, or the area between two curves.
Using the Solver
- Enter your function in terms of x.
- Pick derivative or integral.
- For a derivative at a point, give the x-value. For a definite integral, give the bounds.
- Check the result — graph the original function too if you want a visual gut-check.
Worked Example: A Derivative and an Integral
For f(x) = x³, the derivative is f'(x) = 3x². At x = 2, that's f'(2) = 3(2)² = 12 — the slope of the curve at that exact point.
For the definite integral of x² from 0 to 2, the antiderivative is x³/3. Evaluating from 0 to 2 gives (2³/3) − (0³/3) = 8/3, or about 2.667 — the area under the curve between those two bounds.
Frequently Asked Questions (FAQ)
Does it show steps, or just the answer?
Just the computed result. Work out the steps by hand using your course's rules, then use this to confirm the final number.
Definite and indefinite integrals both?
Yes — give bounds for definite, skip them for the general antiderivative.
What functions does it support?
Polynomial, trig, exponential, log, and combinations of all of it.
Is it free?
Yes, no account needed.
Can I get the derivative at one specific point?
Yes, specify the x-value and it returns the numeric derivative right there.
What about functions with vertical asymptotes?
It'll evaluate near them fine, but a definite integral crossing an asymptote may be improper and need special handling.
Useful for related rates or optimization problems?
Yes — once you've set up the derivative expression, this evaluates it at whatever point you need.
Derivative vs. integral, in plain terms?
Derivative = rate of change. Integral = accumulated total. They're inverses of each other.
Second derivatives?
Take the derivative of your first-derivative result — useful for concavity and inflection points.
Good for AP Calc AB/BC review?
Yes, the core computational skills line up with both exams.