Derivative of $$$\cos{\left(t \right)}$$$
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Your Input
Find $$$\frac{d}{dt} \left(\cos{\left(t \right)}\right)$$$.
Solution
The derivative of the cosine is $$$\frac{d}{dt} \left(\cos{\left(t \right)}\right) = - \sin{\left(t \right)}$$$:
$${\color{red}\left(\frac{d}{dt} \left(\cos{\left(t \right)}\right)\right)} = {\color{red}\left(- \sin{\left(t \right)}\right)}$$Thus, $$$\frac{d}{dt} \left(\cos{\left(t \right)}\right) = - \sin{\left(t \right)}$$$.
Answer
$$$\frac{d}{dt} \left(\cos{\left(t \right)}\right) = - \sin{\left(t \right)}$$$A