Find the derivative of the function. \[ f(t)=66^{t^{3}} \]

To find the derivative of the function \( f(t) = 66^{t^3} \), we can use the chain rule and the property of exponential functions. Recall that the derivative of \( a^{u} \) with respect to \( t \) is given by \( a^{u} \ln(a) \frac{du}{dt} \). Here, we have \( a = 66 \) and \( u = t^3 \). First, we compute the derivative of \( u \): \[ \frac{du}{dt} = 3t^2. \] Now, applying the derivative rule: \[ f'(t) = 66^{t^3} \ln(66) \cdot 3t^2. \] Thus, the derivative is: \[ f'(t) = 3t^2 \cdot 66^{t^3} \ln(66). \]