Find the second derivative of

Question

6x(sin x)

Answer 1

First derivative = y' = d/dx(6xsinx)

                               = 6xd/dx(sinx) + sinxd/dx(6x)   [Since d/dx(uv) = udv/dx + vdu/dx]

                               = 6x(cosx) + sinx(6)                   [Since d/dx(sinx) = cosx, d/dx(6x) = 6]

                               = 6xcosx + 6sinx

Second derivative = d/dx(6xcosx) + d/dx(6sinx)

                             = 6xd/dx(cosx) + cosxd/dx(6x) + 6cosx    [Since d/dx(uv) = udv/dx + vdu/dx]

                             = 6x(-sinx) + cosx(6) + 6cosx                   [Since d/dx(cosx) = -sinx, d/dx(6x) = 6]

                             = -6xsinx + 6cosx + 6cosx

                             = 12cosx - 6xsinx

Therefore second derivative = 12cosx - 6xsinx.