8.01SC | Fall 2016 | Undergraduate
Classical Mechanics
Week 1: Kinematics

1.6 Derivatives

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List of useful derivatives:

  • Derivative of a polynomial function:

    If \(\displaystyle x(t)=At^n \Longrightarrow \frac{dx}{dt}=nAt^{n-1} \)

    where \(A\) and \(n\) are constants.

  • Derivative of an exponential function:

    If \(\displaystyle x(t)=A e^{bt} \Longrightarrow \frac{dx}{dt}=Ab e^{bt} \)

    where \(A\) and \(b\) are constants.

  • Derivative of a logarithmic function:

    If \(\displaystyle x(t)=A\ln(b+ct) \Longrightarrow \frac{dx}{dt}=\frac{Ac}{b+ct} \)

    where \(A\), \(b\) and \(c\) are constants.

  • Derivative of sine:

    If \( \displaystyle x(t)=A\sin(b+ct) \Longrightarrow \frac{dx}{dt}=Ac \cos(b+ct) \)

    where \(A\), \(b\) and \(c\) are constants.

  • Derivative of cosine:

    If \( \displaystyle x(t)=A\cos(b+ct) \Longrightarrow \frac{dx}{dt}=-Ac \sin(b+ct) \)

    where \(A\), \(b\) and \(c\) are constants.

External References

  1. World Web Math
  2. OCW: Single Variable Calculus - Video Lecture 3
  3. Wolfram Alpha

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