Question

How do you find the derivative of `y=(1+e^x)^(-2)`?

Answer 1

`dy/dx=-2e^x(1+e^x)^-3`

Explanation:

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

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

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

`y=(1+e^x)^-2`

`rArrdy/dx=-2(1+e^x)^(-3)xxd/dx(1+e^x)`

`color(white)(rArrdy/dx)=-2e^x(1+e^x)^(-3)`