Find the derivative of the function. $$ f(t)=8 t^{t^{3}} $$ $$ f^{\prime}(t)=\square $$

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Find the first order derivative with respect to $$ t $$ for $$ 8t^{t^{3}} $$.
Evaluate the derivative by following steps:
- step0: Evaluate the derivative:
  $$\frac{d}{dt}\left(8t^{\left(t^{3}\right)}\right)$$
- step1: Simplify:
  $$8\times \frac{d}{dt}\left(t^{\left(t^{3}\right)}\right)$$
- step2: Calculate:
  $$8\left(3t^{t^{3}+2}\ln{\left(t\right)}+t^{t^{3}+2}\right)$$
- step3: Use the distributive property:
  $$8\times 3t^{t^{3}+2}\ln{\left(t\right)}+8t^{t^{3}+2}$$
- step4: Multiply the terms:
  $$24t^{t^{3}+2}\ln{\left(t\right)}+8t^{t^{3}+2}$$
The derivative of the function $$ f(t) = 8t^{t^{3}} $$ with respect to $$ t $$ is given by:

$$ f^{\prime}(t) = 24t^{t^{3}+2}\ln{(t)} + 8t^{t^{3}+2} $$
The derivative of $$ f(t) = 8t^{t^{3}} $$ with respect to $$ t $$ is: $$ f^{\prime}(t) = 24t^{t^{3}+2}\ln{(t)} + 8t^{t^{3}+2} $$

Find the derivative of the function.

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