Question

How do you find the derivative of `f(x)=( 6tanx-10)/secx`?

Answer 1

`f'(x)=6cosx+10sinx`

Explanation:

We can make this simpler by first simplifying the function:

`f(x)=(6tanx-10)/secx=(6(sinx/cosx)-10)/(1/cosx)`

`f(x)=cosx(6sinx/cosx-10)=6sinx-10cosx`

Now, all we need to know is that `d/dxsinx=cosx` and `d/dxcosx=-sinx`. Then:

`f'(x)=6cosx-10(-sinx)=6cosx+10sinx`