## v.s Group Title Find y' and y''. y = eαx sin βx one year ago one year ago

1. malevolence19 Group Title

You need the product rule right?

2. malevolence19 Group Title

And the chain rule, do you know both of these?

3. v.s Group Title

i did like 5 questions like this got all of them wrong

4. malevolence19 Group Title

Well first off, the product rule. If you have two function multiplied together (in this case: x and sin(Bx)) then you apply: $\frac{d}{dx}f(x)*g(x)=f'(x)g(x)+f(x)g'(x)$ As for the chain rule, when you apply it to sin(Bx) you get: $\frac{d}{dx}\sin( \beta x)=\beta \cos(\beta x)$ And you also know that: $\frac{d}{dx}(af(x))=a \frac{d}{dx}f(x)$ So applying all these you get: $y'=\frac{d}{dx}(e \alpha x \sin(\beta x))=e \alpha \frac{d}{dx}x \sin (\beta x)=e \alpha \left[ \frac{d}{dx}(x)\sin(\beta x)+x \frac{d}{dx}\sin(\beta x)\right]$ $=e \alpha \left[ \sin(\beta x) + \beta x \cos(\beta x)\right]$ Now apply those rules again to get y''.

5. v.s Group Title

its wrong

6. malevolence19 Group Title