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

Jan 24, 2016

$f ' \left(x\right) = \frac{\left(2 x + 7\right) \left(x - \cos x\right) - \left(\left({x}^{2} + 7 x - 2\right) \left(1 - \sin x\right)\right)}{x - \cos x} ^ 2$

#### Explanation:

Quatient Rule for Differentiation, let f or and g be differentiable functions at x with $g \left(x\right) \ne 0$, 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
$f ' \left(x\right) = \frac{\left(2 x + 7\right) \left(x - \cos x\right) - \left(\left({x}^{2} + 7 x - 2\right) \left(1 - \sin x\right)\right)}{x - \cos x} ^ 2$
I opted not simplify it further leaving that privilege to you...