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defazajx

Answered question

2021-05-04

Find derivatives for the functions. Assume a, b, c, and k are constants.

y = t^{2} e^{5 t}

Answer & Explanation

dessinemoie

Skilled2021-05-05Added 90 answers

Find derivative of given function:

y^{'} =^{1} {(t^{2})}^{'} {\dot{e}}^{5 t} + t^{2} {\dot{e^{5 t}}}^{'}

=^{2} 2 t {\dot{e}}^{5 t} + t^{2} {\dot{e}}^{5 t} {\dot{5 t}}^{'}

= 2 t e^{5 t} + 5 t^{2} e^{5 t}

= (2 t + 5 t^{2}) e^{5 t}

Rules used:
(1) Product rule
(2) Chain rule

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