The Goal

Find

The Mistake

Find the mistake:

Need a hint? Look carefully at the red part:

The Correction

An Explanation

When the chain rule is applied to the composition of the (natural) exponential function f(t) = e^t and the function g(t), the result is:

In this case g(t) = t², so g'(t) = 2t.
It is usual to write the 2t factor in front of the exponential in the answer.