differential

The linear-approximation notation $dy = f'(x)\,dx$ — the predicted change in $y$ for a small nudge $dx$ in $x$ .

For $y=f(x)$ , the differential $dy = f'(x)\,dx$ estimates the actual change $\Delta y = f(x+dx)-f(x)$ using the tangent line's slope; $dy \approx \Delta y$ for small $dx$ , with the approximation error shrinking faster than $dx$ itself.

Examples

For $y=x^3$ at $x=2$ with $dx=0.01$ : $dy = 3(2)^2(0.01) = 0.12$ .