Question

Question #c181e

Answer 1

Here is a proof using the quotient rule and `d/dx(cosx) = -sinx`

Explanation:

`d/dx(secx) = d/dx(1/cosx)`

`= ((0)(cosx)-(1)(-sinx))/(cosx)^2`

`= sinx/(cosx)^2`

`= 1/cosx * sinx/cosx`

`= secx tanx`

Here's a link to a proof using the definition of derivative

https://socratic.org/questions/how-do-you-use-limit-to-prove-the-derivative-of-secx-secxtanx#132218