Derivatives and Tangent Lines

공식

• Basic Derivative Table

  공식
  $$(x^{n})'=nx^{n-1},\quad (\sin x)'=\cos x,\quad (\cos x)'=-\sin x,\quad (\mathrm{e}^{x})'=\mathrm{e}^{x},\quad (\ln x)'=\frac{1}{x}$$

• Tangent Line at a Point

  공식
  $$y-f(x_{0})=f'(x_{0})(x-x_{0})$$

  적용 조건：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

관련 용어