Question

Find
y' and y''.
y = eαx sin βx

Answer 1

You need the product rule right?

Answer 2

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

Answer 3

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

Answer 4

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''.

Answer 5

its wrong

Answer 6

http://www.wolframalpha.com/input/?i=derivative+of+e+*+a+*+x+*+sin(Bx)

It's not...