Question

What is Differential coefficient of Sin x^2

Answer 1

dy/dx =d/dx(Sin x^2)=2x cosx²

Answer 2

$\bold{\huge{\underline{Question}}}$

What is Differential coefficient of Sin x^2

$\bold{\huge{\underline{Answer-}}}$


$\bf{Definition-}$


Derivative is composed from a function in the same way as the velocity is coordinated by the distance passed by a dynamic particle.



$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{ \bf \: 2x.cos \: {x}^{2} }$


$\bold{\huge{\underline{\underline{Solution-}}}}$


According to the question we need to find Differential coefficient of
x^2


Now,


$\bf \: Let \: \: \: \: \: \: {x}^{2} = t$


So,


$\bf \: \implies \: \: \: \: \: \frac{d}{dx } \: \: {sin \: x}^{2} \\ \\ \\ now \: we \: put \: the \: value \: of \: x^2\: \\ in \:Given\:Formula\\ \\ \\ \implies \bf \: \: \: \frac{d}{dt} sin \: t \\ \\ \\ \implies \: \: \bf \: \frac{d}{dt} sin \: t. \frac{dt}{dx} \\ \\ \\ \implies \: \bf \: \: cos \: t. \frac{d}{dx} {x}^{2} \\ \\ \\ \implies \bf \: \: \: ( {cos \: x}^{2} ) \: 2x \\ \\ \\ \implies \: \bf \: \: 2x. {cos \: x}^{2}$


so,


The Differential coefficient of sin x^2 Is. 2x.cos x^2