It differentiates symbolically, not numerically
The expression is parsed into a tree and the differentiation rules are applied to it, so the answer is an exact formula rather than a number. Product rule, quotient rule and chain rule all compose — x^2·sin(x), sin(x)/x and ln(x²+1) come out as expressions you could have written by hand.
Even x^x works, via logarithmic differentiation: f^g · (g'·ln f + g·f'/f).
The numeric check
Under the results, the symbolic answer is compared against a central difference — the derivative worked out numerically from two nearby function values. They should agree to several decimal places.
When they disagree, it means something real: usually that the function is not smooth at that point. abs(x) at x = 0 is the classic case — it has no derivative there, and the check says so rather than quietly reporting a number.
The tangent is the point
The green dashed line touches the curve at your chosen x, and its slope is the derivative there. Drag the value around and watch it: where the curve rises steeply the tangent is steep, at a peak or trough it goes flat, and that flatness is exactly the f'(x) = 0 you solve for in optimisation problems.
Frequently asked questions
Why is the answer written differently from my textbook?
Because there are many equivalent forms. The result here is simplified mechanically — constants folded, ×1 and +0 removed — but not factorised the way a person would. Both are correct; check by evaluating each at a few points.
Can it integrate?
Not yet. Differentiation is mechanical — a handful of rules applied in order. Integration is genuinely harder: many ordinary-looking functions have no elementary antiderivative at all.
Is anything uploaded?
No. The differentiation happens locally, with nothing logged.
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