List of useful derivatives:
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Derivative of a polynomial function:
If \(\displaystyle x(t)=At^n \Longrightarrow \frac{dx}{dt}=nAt^{n-1} \)
where \(A\) and \(n\) are constants.
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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.
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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.
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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.
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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
