Question

How do you differentiate `f(x)= ( x^2 + 7 x - 2)/ ( cos x )` using the quotient rule?

Answer 1

`f'(x) = ((2x +7)cosx + (x^2+7x-2)sinx)/cos^2 x`

Explanation:

using the `color(blue)" Quotient rule "`

If f(x) `=g(x)/(h(x)) " then " f'(x) = (h(x)g'(x) - g(x)h'(x))/(h(x))^2`

hence`f'(x) = (cosx d/dx(x^2+7x-2) - (x^2+7x-2) d/dx(cosx))/(cosx)^2`

`= (cosx(2x+7) - (x^2+7x-2)(-sinx))/cos^2x`

`=( (2x+7)cosx + (x^2+7x-2)sinx)/cos^2x`