Question

How do you differentiate `x/cos x`?

Answer 1

Here we would use the quotient rule of differentiation.

We have the following rule,

`d/dx(u/v) = (v(du)/dx - u(dv)/dx)/v^2`

Here, `u(x) = x` and `v(x) = Cos x`

Explanation:

Putting `u(x) = x` and `v(x) = Cos x`

Let, `y = x/(Cos x) = u/v`

Thus, `(dy)/dx = d/dx(u/v) = (v(du)/dx - u(dv)/dx)/v^2`

`implies (dy)/dx = (Cos x + x*Sinx)/Cos ^2x`

Where `d/dx (x) = 1` and `d/dx (Cos x) = - Sin x` which are standard derivatives obtained from first principle.