Find the differential of each function.

Question

a) y=tan(sqrt(3t))

dy=?

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

dy=?

Answer 1

Use chain rule on the first problem.

dy=sec²((3t)^1/2) (1 / 2)(3t)^(-1/2) (3)dx ;

dy = 3sec²((3t)^1/2) / 2(3t)^1/2 dx

For the second problem use quotient rule

dy = [(-2v)(5+v²)-(5-v²)(2v)] / (5+v²)² dx

dy=(-10v-2v³-10v+2v³) / (5+v²)²dx

dy = -20v / (5+v²)²_dx