What is the derivative of te(-t2)?

Answer 1

Use the product and chain rules:

d/dt te^(-t²) = (d/dt t)e^(-t²) + t(d/dt e^(-t²))

= 1 × e^(-t²) + t × e^(-t²) × d/dt -t²

= e^(-t²) (1 + t × -2t)

= (1 - 2t²)e^(-t²)

Answer 2

It is e^(-t2) - 2t2*e^(-t2) .