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Next exam on November 14 – 15, 2026:
All concepts

Derivatives and Tangent Lines

导数与切线

Derivative table for elementary functions, derivative values at a point, the tangent-line equation, and using f′ to determine monotonicity.

Not yet examined18 in mock papers20 practice

Formulas

  • Basic Derivative Table

    Formula
    (xn)′=nxn−1,(sin⁡x)′=cos⁡x,(cos⁡x)′=−sin⁡x,(ex)′=ex,(ln⁡x)′=1x(x^{n})'=nx^{n-1},\quad (\sin x)'=\cos x,\quad (\cos x)'=-\sin x,\quad (\mathrm{e}^{x})'=\mathrm{e}^{x},\quad (\ln x)'=\frac{1}{x}

  • Tangent Line at a Point

    Formula
    y−f(x0)=f′(x0)(x−x0)y-f(x_{0})=f'(x_{0})(x-x_{0})

    Applies when：f differentiable at x₀; point of tangency (x₀, f(x₀))

    x₀
    x-coordinate of the point of tangency
    f'(x₀)
    derivative at x₀ — the tangent slope

Real-exam evidence

Recorded past-paper appearances are listed below; online verification is labelled separately.

No question in the past papers on record tests this concept yet. It is in the syllabus, so it can still come up.

18 questions across 10 mock papers — our own papers, so a coverage signal rather than real-exam evidence

20 related practice questions availablePractise free: Calculus

Sitting evidence comes from the CSCA past papers on record; questions whose original paper is missing are excluded, and sprint papers are deliberately not counted.

Glossary

derivative