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

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