Question

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

Derivatives

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

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