If $x=\sqrt{a^{\sin ^{-1} t}}$ and $y=\sqrt{a^{\cos ^{-1} t}}$ then $\frac{d y}{d x}=$

JEE MATHEMATICS MCQ: DIFFERENTIATION

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Application +4 | -1

x=\sqrt{a^{\sin ^{-1} t}}

and

y=\sqrt{a^{\cos ^{-1} t}}

then

\frac{d y}{d x}=

View answer and explanation

Correct option: D

-\frac{y}{x}

Option D (

\frac{-y}{x}

) is correct because multiplying the given equations and differentiating leads to this result.

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