Find the derivative of the following functions s(t)=cos⁡2t

Step 1
According to the question, we have to find derivative of the function ${\displaystyle s\left(t\right)={\cos 2}^t}$
The derivative of a function s(t) of a variable t is a measure of the rate at which the value s of the function changes with respect to the change of the variable t.
To differentiate the function, we have to arrange the variable term on one side, then we can differentiate with respect to the appropriate variable.
Step 2
Rewrite the given expression,
${\displaystyle s\left(t\right)={\cos 2}^t}$
Now differentiating the above function with respect to t,
${\displaystyle s^{\prime }\left(t\right)=-{\sin 2}^t\cdot \frac{d}{dt}\left(2^t\right)}$
${\displaystyle =-{\sin 2}^t\cdot 2^t\cdot \ln \left(2\right)}$
Hence, the derivative of the function ${\displaystyle s\left(t\right)={\cos 2}^{t}is{s}^{\prime }\left(t\right)=-{\sin 2}^t\cdot 2^t\cdot \ln t}$