Question

How do you find the derivative of `y =(x+2)/cosx`?

Answer 1

`dy/dx=(cosx+sinx(x+2))/cos^2x`

Explanation:

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

If `y=(g(x))/(h(x))rArr dy/dx=(h(x)g'(x)-g(x)h'(x))/(h(x))^2`
`color(blue)"------------------------------------------------------------"`

here `g(x)=x+2rArrg'(x)=1`

and `h(x)=cosxrArrh'(x)=-sinx`
`color(blue)"-----------------------------------------------------------------"`

`rArrdy/dx=(cosx.1-(x+2)(-sinx))/cos^2x`

`=(cosx+sinx(x+2))/cos^2x`