If $y = \log (\sin \,({x^2})),0 < x < \frac{\pi }{2},$ then $\frac{{dy}}{{dx}}$ at $x = \frac{{\sqrt \pi }}{2}$ is

JEE MATHEMATICS MCQ: DIFFERENTIATION

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Application +4 | -1

y = \log (\sin \,({x^2})),0 < x < \frac{\pi }{2},

then

\frac{{dy}}{{dx}}

x = \frac{{\sqrt \pi }}{2}

View answer and explanation

Correct option: D

\sqrt \pi

Option D (

\sqrt{\pi}

) is correct because it is the value obtained after differentiating the given function and substituting the given value of x.

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v\frac{{\partial z}}{{\partial x}} + \frac{{\partial z}}{{\partial y}}