The Goal

Find

The Mistake

Find the mistake:

(Roll the mouse over the math to see a hint in red)

The Correction

(Roll the mouse over the area above to see the correction in blue)

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.