Question

For \[y=\mathrm{A}\sin x+\mathrm{B}\cos x\], what is \[\frac{d^2y}{dx^2}\]?

Options

• \[\mathrm{A}\cos x-\mathrm{B}\sin x=y\]

• \[-\mathrm{A}\cos x+\mathrm{B}\sin x=-y\]

• \[-\mathrm{A}\sin x-\mathrm{B}\cos x=-y\]

• \[\mathrm{A}\sin x-\mathrm{B}\cos x=y\]

Answer 1

Differentiating \[\mathrm{A}\cos x-\mathrm{B}\sin x\] gives \[-\mathrm{A}\sin x-\mathrm{B}\cos x\]. Since \[y=\mathrm{A}\sin x+\mathrm{B}\cos x\], this result equals \[-y\].