Question

How do you find the derivative of `2e^(-0.7x)sin(2pix)`?

Answer 1

`=2e^(-0.7x)(-0.7sin(2pix)+2picos(2pix))`

Explanation:

You would apply the rules:

`f(x)=g(x)*h(x)->f'(x)=g'(x)*h(x)+g(x)*h'(x)`
`f(x)=e^g(x)->f'(x)=e^g(x)*g'(x)`
`f(x)=sin(g(x))->f'(x)=cos(g(x))*g'(x)`
`f(x)=kg(x)->f'(x)=kg'(x)`

and get

`y'=2e^(-0.7x)*(-0.7)*sin(2pix)+2e^(-0.7x)*cos(2pix)*2pi`

`=2e^(-0.7x)(-0.7sin(2pix)+2picos(2pix))`