What is the derivative of $${\sec ^2}({\tan ^{ - 1}}x)$$ with respect to x ?

If f(x) = sin (cos x), then f'(x) is equal to

Let  $x = \sec \theta - \cos \theta \text{ and } y = \sec^4 \theta - \cos^4 \theta \\ $ 

What is $(\frac{dy}{dx})^2$ equal to?

Let  $x = \sec \theta - \cos \theta \text{ and } y = \sec^4 \theta - \cos^4 \theta \\ $ 

What  $\left[ \frac{x^2+4}{y^2+4} \frac{dy}{dx} \left( x^2+4 \frac{d^2y}{dx^2} - 16y \right) \right] $  equal to?