Question

Differentiate
Y= sec(tan(x^1/2))

Answer 1

Y= sec(tan(x^1/2))

dY/dx = d/dx{sec(tan(x^1/2))}

= sec(tan(x^1/2)).tan(tan(x^1/2)).d/dx(tan(x^1/2))

= sec(tan(x^1/2)).tan(tan(x^1/2)).sec^2(x^1/2). d/dx(x^1/2)

= sec(tan(x^1/2)).tan(tan(x^1/2)).sec^2(x^1/2). 1/(2√x) (ans.)

Answer 2

$y = sec(tan \sqrt{x} ) \\ \\ \frac{dy}{dx} = sec(tan \sqrt{x} )tan(tan \sqrt{x} ) \frac{d}{dx} tan \sqrt{x} \\ \\ \frac{dy}{dx} = sec(tan \sqrt{x} )tan(tan \sqrt{x} ) {sec}^{2} \sqrt{x} \frac{d}{dx} \sqrt{x} \\ \\ \frac{dy}{dx} = sec(tan \sqrt{x} )tan(tan \sqrt{x} ) {sec}^{2} \sqrt{x} \frac{1}{2 \sqrt{x} }$