Question

Given \[y=a\sin(x+b)\], what is \[\frac{d^{2}y}{dx^{2}}\]?

Options

• \[\frac{d^{2}y}{dx^{2}}=-a\sin(x+b)\]

• \[\frac{d^{2}y}{dx^{2}}=a\sin(x+b)\]

• \[\frac{d^{2}y}{dx^{2}}=-a\cos(x+b)\]

• \[\frac{d^{2}y}{dx^{2}}=a\cos(x+b)\]

Answer 1

Differentiate \[a\cos(x+b)\] with respect to \[x\]. Since the derivative of cosine is negative sine, the result is \[-a\sin(x+b)\].