Question

Differentiate

$\frac{\cos x-\sin x}{14\sin 2x}$

Answer 1

Consider the function

$\frac{\cos x-\sin x}{14\sin 2x}$

Apply the quotient rule

$\begin{array}{c}\frac{d}{dx}\left(\frac{\cos x-\sin x}{14\sin 2x}\right)=\frac{\frac{d}{dx}\left(\cos x-\sin x\right)\times 14\sin 2x-\left(\cos x-\sin x\right)\frac{d}{dx}14\sin 2x}{{\left(14\sin 2x\right)}^2}\\ =\frac{\left(-sinx-\cos x\right)\times 14\sin 2x-\left(\cos x-\sin x\right)28\cos 2x}{{\left(14\sin 2x\right)}^2}\end{array}$

Hence, $f^{\prime }\left(x\right)=\frac{\left(-sinx-\cos x\right)\times 14\sin 2x-\left(\cos x-\sin x\right)28\cos 2x}{{\left(14\sin 2x\right)}^2}$