Question

Differenciation of 1 devide by Cosx by product rule?

Answer 1

`sec(x)tan(x)`

Explanation:

No need to use product rule here.

The original problem is `d/dx(1/cos(x))`. The trick here is to use the reciprocal function of `cos(x)`, that is `sec(x)`. So, the problem becomes `d/dx(sec(x))`.

This is a common trigonometric derivative, and it equates to `sec(x)tan(x)`.

Therefore, `d/dx(sec(x))=sec(x)tan(x)`

or

`d/dx(1/cos(x))=sec(x)tan(x)`

Source:

http://www.sosmath.com/calculus/diff/der03/der03.html

Answer 2

`(d(1) /Cosx)/dx` by product rule.

you cant really apply the product rule directly here, so we'll change it a bit.

`(d(1xx secx))/dx`

`=(1)'(secx) + (secx)'(1)` (applying product rule,)

`= (0 xx secx) + (secxtanx xx1)`

`=0 + secxtanx = secxtanx`

Note that here, `(d(1xx secx))/dx` is just `(d( secx))/dx` which could have been directly written as `secxtanx`.