Question

Find derivatives of the functions defined as follows.y=(t^2 e^(2t))/(t+e^(3t))

Derivatives
ANSWERED
asked 2020-12-28

Find derivatives of the functions defined as follows. \(y=(t^2 e^{(2t)})/(t+e^{(3t)})\)

Expert Answers (1)

2020-12-29

\(dy/dt=((t+e^{(3t)})(2t^2 e^{(2t)}+2te^{(2t)})-(t^2 e^{(2t)})(1+3e^{(3t)}))/((t+e^{(3t)})^2)\)
\(=(2t^3 e^{(2t)}+2t^2 e^{(2t)}+2t^2 e^{(5t)}+2t e^{(5t)}-t^2 e^{(2t)}+3t^2 e^{(5t)})/((t+e^{(3t)})^2)\)
\(=((5t^2+2t)e^{(5t)}+(2t^3+t^2)e^{(2t)})/((t+e^{(3t)})^2)\)

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