Question

Find derivatives for the functions. Assume a, b, c, and k are constants. y=t^{2}e^{5t}

Derivatives
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asked 2021-05-04
Find derivatives for the functions. Assume a, b, c, and k are constants.
\(\displaystyle{y}={t}^{{{2}}}{e}^{{{5}{t}}}\)

Answers (1)

2021-05-05
Find derivative of given function:
\(\displaystyle{y}'=^{{{1}}}{\left({t}^{{{2}}}\right)}'\dot{{e}}^{{{5}{t}}}+{t}^{{{2}}}\dot{{{e}^{{{5}{t}}}}}'\)
\(\displaystyle=^{{{2}}}{2}{t}\dot{{e}}^{{{5}{t}}}+{t}^{{{2}}}\dot{{e}}^{{{5}{t}}}\dot{{{5}{t}}}'\)
\(\displaystyle={2}{t}{e}^{{{5}{t}}}+{5}{t}^{{{2}}}{e}^{{{5}{t}}}\)
\(\displaystyle={\left({2}{t}+{5}{t}^{{{2}}}\right)}{e}^{{{5}{t}}}\)
Rules used:
(1) Product rule
(2) Chain rule
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