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CBSE Class 12 · 2024 · DifferentiationMultiple Choice

If

sin (x y) = 1

, then

\frac{d y}{d x}

is equal to:

(A) $\frac{x}{y}$
(B) $- \frac{x}{y}$
(C) $\frac{y}{x}$
(D) $- \frac{y}{x}$ ✓ Correct

Answer: (D)

Solution

sin (x y) = 1 \Rightarrow x y = \frac{π}{2}

, a constant.
Differentiate the relation

x y = constant

implicitly with respect to

x

:

x \frac{d y}{d x} + y = 0

\frac{d y}{d x} = - \frac{y}{x}

CBSE Class 12 Board · 2024 · Single correct option

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