v.s Group Title Find y' and y''. y = eαx sin βx 2 years ago 2 years ago

1. malevolence19

You need the product rule right?

2. malevolence19

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

3. v.s

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

4. malevolence19

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

its wrong

6. malevolence19