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

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Let $$ f(t)=66^{t^3} $$. We can differentiate this function by using the general formula for the derivative of an exponential function with a non-constant exponent:

$$
\frac{d}{dt}\left(a^{g(t)}\right)=a^{g(t)}\ln(a)\cdot g'(t)
$$

In this case, we have:
- $$ a=66 $$
- $$ g(t)=t^3 $$

First, compute $$ g'(t) $$:

$$
g'(t)=\frac{d}{dt}\left(t^3\right)=3t^2
$$

Now, applying the formula:

$$
f'(t)=66^{t^3}\ln(66)\cdot 3t^2
$$

Thus, the derivative of the function is:

$$
f'(t)=3t^2\ln(66) \cdot 66^{t^3}
$$
The derivative of $$ f(t) = 66^{t^3} $$ is $$ f'(t) = 3t^2 \ln(66) \cdot 66^{t^3} $$.

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

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