(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 = (5v^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