Question

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

Answer 1

`f'(x) = [(2x+ 7)(x-cosx) - ((x^2 + 7x - 2)(1-sinx))]/(x-cosx)^2`

Explanation:

Quatient Rule for Differentiation, let f or and g be differentiable functions at x with `g(x) != 0`, then f/g is differentiable at x and
`[f(x)g(x)]'= [g(x)f'(x)−f(x)g'(x)]/ [g(x)]^2`

Now `h(x) = x^2 + 7x - 2; g(x) = x-cosx`
`h'(x) =2x +7; g'(x) = 1 - sinx`
`f'(x) = [(2x+ 7)(x-cosx) - ((x^2 + 7x - 2)(1-sinx))]/(x-cosx)^2`
I opted not simplify it further leaving that privilege to you...