8.01SC | Fall 2016 | Undergraduate

# Classical Mechanics

Week 1: Kinematics

## 1.6 Derivatives

« Previous | Next »

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

« Previous | Next »

Fall 2016
Lecture Videos
Problem Sets
Online Textbook