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Implicit Differentiation

Find the deri...

Question

Find the derivative of $e^{x} + e^{y} = e^{x + y}$

A

- e^{x - y}

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B

e^{x - y}

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C

- e^{y - x}

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D

e^{y - x}

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Solution

The correct option is C $- e^{y - x}$
Given, $e^{x} + e^{y} = e^{x + y} = e^{x} e^{y}$
$\Rightarrow e^{- y} + e^{- x} = 1$
On differentiating, we get
$- e^{- y} \frac{d y}{d x} + e^{- x} (- 1) = 0$
$\Rightarrow \frac{d y}{d x} = \frac{e^{- x}}{- e^{- y}}$
$\Rightarrow \frac{d y}{d x} = - e^{y - x}$

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Similar questions

e^{x} + e^{y} = e^{x + y}

\frac{d y}{d x} + e^{y - x} = 0

e^{x} + e^{y} = e^{x + y}

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

e^{x} + e^{y} = e^{x + y}

\frac{d y}{d x} = - \frac{e^{x} (e^{y} - 1)}{e^{y} (e^{x} - 1)}

e^{x} + e^{y} = e^{x + y}

\frac{d y}{d x} + e^{y - x} = 0

Q. The general solution of the differential equation

\frac{d y}{d x} = e^{x + y}

, is
(a) e^x+ e^−y = C
(b) e^x + e^y = C
(c) e⁻^x + e^y = C
(d) e^−x + e^−y = C

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