Find the differential of each function. (a) y = tan√(3t) and (b) y = (5 − v^2)/ (5 + v^2)?

NetherCraft 0

(a) y = tan√(3t)

dy =

(b) y = (5 − v^2)/ (5 + v^2)

dy =

im getting answers sec^2√t / 3√t dt and -4v / (5 +v^2)^2 dv

and it tells me its wrong please help

1 Answer

  • If:

    y = tan(sqrt(3t)), then:

    dy/dt = (sqrt(3)(1/2)/sqrt(t))(sec(sqrt(3x)))^2

    dy = sqrt(3/(4t))*(sec(sqrt(3x)))^2 dt


    If y = (5-v^2)/(5+v^2)

    Simplify the right hand side by expanding in terms of partial fractions:

    y = 10/(5+v^2) – 1

    dy/dv = 10(-1)(2v)/(5 + v^2)^2

    dy = -20v/(5 + v^2) dv

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