If 2 x + 2 y = 2 x + y then the value of d y d x a t x = y = 1 i s Options: A . &nbsp0 B . &nbsp- 1 C . &nbsp1 D . &nbsp2

Answer: Option B : B 2 x + 2 y = 2 x + y ∴ 2 x . l o g e 2 + 2 y . l o g e 2 d y d x = 2 x + y . l o g e 2 ( 1 + d y d x ) ∴ d y d x = 2 x + y − 2 x 2 y − 2 x + y d y d x | x = y = 1 = − 1

If 2x+2y=2x+y then the value of dydx at x=y=1 is

Question

2^{x} + 2^{y} = 2^{x + y}

then the value of

\frac{d y}{d x} a t x = y = 1 i s

Options:

A . 0

B . - 1

C . 1

D . 2

Answer: Option B
:
B

2^{x} + 2^{y} = 2^{x + y}

∴ 2^{x} . l o g_{e} 2 + 2^{y} . l o g_{e} 2 \frac{d y}{d x} = 2^{x + y} . l o g_{e} 2 (1 + \frac{d y}{d x})

∴ \frac{d y}{d x} = \frac{2^{x + y} - 2^{x}}{2^{y} - 2^{x + y}}

\frac{d y}{d x} |_{x = y = 1} = - 1

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