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JEE MATHEMATICS MCQ: DIFFERENTIATION

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Application +4 | -1
If y=f(2x−1x2+1)y=f\left(\frac{2 x-1}{x^2+1}\right) and f′(x)=sin⁡x2f^{\prime}(x)=\sin x^2, then dydx=\frac{d y}{d x}=
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Correct option: D
−2x2+2x+2(x2+1)2sin⁡(2x−1x2+1)2\frac{-2 x^2+2 x+2}{\left(x^2+1\right)^2} \sin \left(\frac{2 x-1}{x^2+1}\right)^2
Option D (−2x2+2x+2(x2+1)2\frac{{-2 x^2+2 x+2}}{{(x^2+1)^2}} \sin (2x−1x2+1\frac{{2 x-1}}{{x^2+1}})2) is correct because it is the result of applying the chain rule to find the derivative of the composite function.

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