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Derivative of $$$\frac{\cos{\left(t \right)}}{3}$$$

The calculator will find the derivative of $$$\frac{\cos{\left(t \right)}}{3}$$$, with steps shown.

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Find $$$\frac{d}{dt} \left(\frac{\cos{\left(t \right)}}{3}\right)$$$.

Solution

Apply the constant multiple rule $$$\frac{d}{dt} \left(c f{\left(t \right)}\right) = c \frac{d}{dt} \left(f{\left(t \right)}\right)$$$ with $$$c = \frac{1}{3}$$$ and $$$f{\left(t \right)} = \cos{\left(t \right)}$$$:

$${\color{red}\left(\frac{d}{dt} \left(\frac{\cos{\left(t \right)}}{3}\right)\right)} = {\color{red}\left(\frac{\frac{d}{dt} \left(\cos{\left(t \right)}\right)}{3}\right)}$$

The derivative of the cosine is $$$\frac{d}{dt} \left(\cos{\left(t \right)}\right) = - \sin{\left(t \right)}$$$:

$$\frac{{\color{red}\left(\frac{d}{dt} \left(\cos{\left(t \right)}\right)\right)}}{3} = \frac{{\color{red}\left(- \sin{\left(t \right)}\right)}}{3}$$

Thus, $$$\frac{d}{dt} \left(\frac{\cos{\left(t \right)}}{3}\right) = - \frac{\sin{\left(t \right)}}{3}$$$.

Answer

$$$\frac{d}{dt} \left(\frac{\cos{\left(t \right)}}{3}\right) = - \frac{\sin{\left(t \right)}}{3}$$$A

Related Notes: Definition of Derivative , Derivatives of Elementary Functions , Table of Derivatives , Related Rates , Studying Derivative Graphically , Optimization Problems , Applications to Economics , Constant Multiple Rule , Sum and Difference Rules , Product Rule , Quotient Rule , Chain Rule , Derivative of Inverse Function