Question

If \[y=\mathrm{A}\sin x+\mathrm{B}\cos x\], what is \[\frac{dy}{dx}\]?

Options

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

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

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

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

Answer 1

Differentiating \[\mathrm{A}\sin x\] gives \[\mathrm{A}\cos x\]. Differentiating \[\mathrm{B}\cos x\] gives \[-\mathrm{B}\sin x\], so \[\frac{dy}{dx}=\mathrm{A}\cos x-\mathrm{B}\sin x\].