Let $x^{c o s y} + y^{c o s x} = 5$ . Then

at x = 0, y = 0, y’ = 0

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at x = 0, y = 1, y’ = 0

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at x = y = 1, y’ = – 1

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at x = 1, y = 0, y’ = 1

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Solution

The correct option is C at x = y = 1, y’ = – 1
$x^{c o s y} + y^{c o s x} = 5$
$\Rightarrow e^{c o s y l o g_{e} x} + e^{c o s y l o g_{e} y} = 5 ∴ e^{c o s y l o g_{e} x} {\frac{c o s y}{x} - l o g_{e} x s i n y \frac{d y}{d x}} + e^{c o s y l o g_{e} y} {\frac{c o s x}{y} \frac{d y}{d x} - s i n x l o g_{e} y} = 0$
Put x=0,y=0,then $(c o s 1 - 0) + (c o s 1 \frac{d y}{d x} - 0) = 0 ∴ \frac{d y}{d x} = - 1$
or $y^{'} = - 1$

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