Question

Derivative

Answer 1

\[4te ^{t}\]

Answer 2

\( \dfrac{d}{dt}(uv) = uv' + vu' \)

\( \dfrac{d}{dt} (ku) = k \dfrac{d}{dt}u \)

Answer 3

\( \dfrac{d}{dt} (4te^t) \)

\(= 4 \dfrac{d}{dt} (te^t) \)

\( = 4 (t \cdot \dfrac{d}{dt} e^t + e^t \cdot \dfrac{d}{dt} t )\)

\( = 4 (t \cdot e^t + e^t \cdot 1 )\)

\( = 4 e^t (t + 1 )\)