If xcos y+ycos x=5. Then

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Question

I f x^{c o s y} + y^{c o s x} = 5.

Then

Options:

A . at x = 0, y = 0, y’ = 0

B . at x = 0, y = 1, y’ = 0

C . at x = y = 1, y’ = – 1

D . at x = 1, y = 0, y’ = 1

Answer: Option C
:
C

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 x 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 x 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

P u t x = y = 1, (c o s 1 - 0) + (c o s 1 \frac{d y}{d x} - 0) = 0

∴ \frac{d y}{d x} = - 1

o r y^{'} = - 1

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