For the function y = (1+e^t)*ln t, we can find the derivative with respect to t by using the product rule

y' = [(1+e^t)*ln t]'

=> [(1+e^t)]'*ln t + (1+e^t)*[ln t]'

=> e^t*ln t + (1 + e^t)/t

=> (t*e^t*ln t + e^t + 1)/t

For the function y = [(10^t)(ln t)]

y' = (10^t)'*ln t + 10^t*(ln t)'

=> 10^t*ln t*ln t + (10^t)/t

**The derivative of (1+e^t)*ln t is (t*e^t*ln t + e^t + 1)/t and that of [(10^t)(ln t)] is 10^t*ln t*ln t + (10^t)/t**

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