Question

How do you differentiate `y=e^((2x)/3)`?

Answer 1

`dy/dx=2/3e^((2x)/3)`

Explanation:

`color(orange)"Reminder"`

`d/dx(e^x)=e^x`

and using the `color(blue)"chain rule"`

`color(red)(|bar(ul(color(white)(a/a)color(black)(d/dx(e^(g(x)))=e^(g(x))g'(x))color(white)(a/a)|)))`

`rArrdy/dx=e^((2x)/3).d/dx(2/3x)=2/3e^((2x)/3)`