calculus

fin derivative of the function

(t+e^t)(4- sqrt t)

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  1. Use the product rule
    d/dt (u*v) = u*dv/dt + v*du/dt

    and you get
    (t + e^t)[-1/(2*sqrt t)]
    + (1 + e^t)(4 - sqrt t)

    Or you could multiply out u(t)*v(t) and differentiate it term by term

    u*v = 4t + 4e^t -t^3/2 -e^t*t^1/2

    d/dt(u*v) = 4 + 4e^t -(3/2)t^1/2 -e^t*t^1/2 -(1/2)e^t/t^1/2

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