Question

Derivative of `e^x-e^-x`?

Answer 1

`e^x+e^-x`

Explanation:

`color(red)(d/(dx)(e^x)=e^x`
`y=e^x-e^-x=>(dy)/(dx)=e^x-e^-x*d/(dx)(-x)` `=e^x-e^-x(-1)=e^x+e^-x`

Answer 2

`e^x+e^(-x)`

Explanation:

`"differentiate "e^(-x)" using the "color(blue)"chain rule"`

`"Given "y=f(g(x))" then"`

`dy/dx=f'(g(x))xxg'(x)larrcolor(blue)"chain rule"`

`rArrd/dx(e^(-x))=e^(-x)xxd/dx(-x)=-e^(-x)`

`rArrd/dx(e^x-e^(-x))`

`=e^x-(-e^(-x))=e^x+e^(-x)`

Answer 3

`=e^x+e^-x`

Explanation:

`d/dx(e^x-e^-x)`
`=d/dx(2sinh x)` (definition of sinh x)
`=2cosh x` (Because `d/dx sinhx = cosh x` and vice versa)
`=e^x+e^-x` (definition of cosh x)