Question

Given \[y=a\sin(x+b)\], where \[a,b\in R\], what is \[\frac{dy}{dx}\]?

Options

• \[\frac{dy}{dx}=-a\cos(x+b)\]

• \[\frac{dy}{dx}=-a\sin(x+b)\]

• \[\frac{dy}{dx}=a\sin(x+b)\]

• \[\frac{dy}{dx}=a\cos(x+b)\]

Answer 1

The derivative of \[\sin(x+b)\] is \[\cos(x+b)\]. Since \[a\] is constant, \[\frac{dy}{dx}=a\cos(x+b)\].