Question

How do you differentiate `g(x) =e^(1-x^2)sec` using the product rule?

Answer 1

I assume this should be `g(x) =e^(1-x^2)secx`

Explanation:

Note that

`d/dx(e^(1-x^2))` may be found using thechain rule,

`d/dx(e^(1-x^2)) = -2xe^(1-x^2)`

And `d/dx(secx) = secxtanx`, so

`d/dx(e^(1-x^2)) = -2xe^(1-x^2)secx+e^(1-x^2)secx tanx`

Factor and rewrite to taste.