Question

# Find derivatives for the functions. Assume a, b, c, and k are constants. H(t)=(at^{2}+b)e^{−ct}

Derivatives
Find derivatives for the functions. Assume a, b, c, and k are constants.
$$\displaystyle{H}{\left({t}\right)}={\left({a}{t}^{{{2}}}+{b}\right)}{e}^{{−{c}{t}}}$$

$$\displaystyle{H}'{\left({t}\right)}={\left[{\left({a}{t}^{{{2}}}+{b}\right)}{e}^{{-{c}{t}}}\right]}'$$
$$\displaystyle={\left[{\left({a}{t}^{{{2}}}+{b}\right)}\right]}'{e}^{{-{c}{t}}}+{\left({a}{t}^{{{2}}}+{b}\right)}{\left[{e}^{{-{c}{t}}}\right]}'$$
$$\displaystyle={2}{a}{t}{e}^{{-{c}{t}}}-{c}{\left({a}{t}^{{{2}}}+{b}\right)}{e}^{{-{c}{t}}}$$