Question

find derivate with respect to x ​

Answer 1

Step-by-step explanation:

$y = { \sin }^{2}x - { \cos}^{2}x \\ \frac{dy}{dx} = \frac{d}{dx} ({ \sin }^{2}x - { \cos}^{2}x) \\ = \frac{d}{dx} ({ \sin }^{2}x) - \frac{d}{dx} ( { \cos}^{2}x) \\ = \frac{d}{dx} { (\sin \: x)}^{2} - \frac{d}{dx} { (\cos \: x)}^{2} \\ = 2 \sin\: x \times \frac{d}{dx} ( \sin \: x) - 2 \cos\: x \times \frac{d}{dx} ( \cos \: x) \\ =( 2 \sin \: x \times \cos \: x) - (2 \cos \: x \times ( - \sin \: x)) \\ = 2 \sin \: x \cos \: x + 2 \sin \: x \cos \: x \\ = 4 \sin \: x \cos \: x$