# How do you differentiate f(x) = (-11x) / (sin(x)+cos(x))?

Apr 29, 2018

$f ' \left(x\right) = \frac{\left(11 \sin x\right) \left(x + 1\right) + \left(11 \cos x\right) \left(1 - x\right)}{\sin x + \cos x} ^ 2$

#### Explanation:

$f \left(x\right) = \frac{- 11 x}{\sin x + \cos x}$

$f ' \left(x\right) = \frac{\left(\cos x - \sin x\right) \left(- 11 x\right) - \left(\sin x + \cos x\right) \times \left(- 11\right)}{\sin x + \cos x} ^ 2$

$f ' \left(x\right) = \frac{- 11 x \cos x + 11 x \sin x + 11 \sin x + 11 \cos x}{\sin x + \cos x} ^ 2$

$f ' \left(x\right) = \frac{\left(11 \sin x\right) \left(x + 1\right) + \left(11 \cos x\right) \left(1 - x\right)}{\sin x + \cos x} ^ 2$

Remember:
IF $f \left(x\right) = \frac{u}{v}$
THEN $f ' \left(x\right) = \frac{v ' u - v u '}{v} ^ 2$