If 2x-2y-2x-y then the value of d y-d x at x-y-1 is

The correct option is A 1 2^x + 2^y = 2^x + y ∴ 2^x. log_e 2 + 2^y. log_e 2 dy/dx = 2^x+y. log_e 2 (1 + dy/dx ) ∴dy/dx = 2^x+y 2^x/2^y 2^x+y dy/dx|_x = ...

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Byju's Answer

Standard XII

Mathematics

Implicit Differentiation

If 2x+2y=2x+y...

Question

If $2^{x} + 2^{y} = 2^{x + y}$ then the value of $\frac{d y}{d x} a t x = y = 1 i s$

- 1

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Solution

The correct option is A - 1
$2^{x} + 2^{y} = 2^{x + y}$
$∴ 2^{x} . l o g_{e} 2 + 2^{y} . l o g_{e} 2 \frac{d y}{d x} = 2^{x + y} . l o g_{e} 2 (1 + \frac{d y}{d x})$
$∴ \frac{d y}{d x} = \frac{2^{x + y} - 2^{x}}{2^{y} - 2^{x + y}}$
$\frac{d y}{d x} |_{x = y = 1} = - 1$

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

The correct option is A - 1 2x+2y=2x+y ∴2x.loge 2+2y.loge 2dydx=2x+y.loge 2(1+dydx) ∴dydx=2x+y−2x2y−2x+y dydx|x=y=1=−1

If $2^{x} + 2^{y} = 2^{x + y}$ then the value of $\frac{d y}{d x} a t x = y = 1 i s$

The correct option is A - 1
$2^{x} + 2^{y} = 2^{x + y}$
$∴ 2^{x} . l o g_{e} 2 + 2^{y} . l o g_{e} 2 \frac{d y}{d x} = 2^{x + y} . l o g_{e} 2 (1 + \frac{d y}{d x})$
$∴ \frac{d y}{d x} = \frac{2^{x + y} - 2^{x}}{2^{y} - 2^{x + y}}$
$\frac{d y}{d x} |_{x = y = 1} = - 1$