DETERMINE SECOND DERIVATIVES

Question

Determine y’’ given: y = 3^ax + sin (bx) where a, b E R are constants.

Answer 1

y = 3^ax + sin(bx)

y' = (ln3)3^ax(ax)' + cos(bx)(bx)' = a(ln3)3^ax + bcos(bx)

y" = a(ln3)(ln3)3^ax(ax)' + b(-sin(bx))(bx)' = (aln3)²3^ax - b²sin(bx)