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

Feb 22, 2016

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

#### Explanation:

using the $\textcolor{b l u e}{\text{ Quotient rule }}$

If f(x) $= g \frac{x}{h \left(x\right)} \text{ then } f ' \left(x\right) = \frac{h \left(x\right) g ' \left(x\right) - g \left(x\right) h ' \left(x\right)}{h \left(x\right)} ^ 2$

hence$f ' \left(x\right) = \frac{\cos x \frac{d}{\mathrm{dx}} \left({x}^{2} + 7 x - 2\right) - \left({x}^{2} + 7 x - 2\right) \frac{d}{\mathrm{dx}} \left(\cos x\right)}{\cos x} ^ 2$

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

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