If x y = e x − y then d y d x = Options: A . &nbsp(1+In x)−1 B . &nbsp(1+In x)−2 C . &nbspIn x(1+In x)−2 D . &nbspNone of these

Answer: Option C : C S i n c e , x y = e x − y ⇒ y l n x = x − y ∴ y = x 1 + I n x ∴ d y d x = l n x ( 1 + I n x ) 2

If xy=ex−y then dydx=

Question

x^{y} = e^{x - y}

then

\frac{d y}{d x} =

Options:

A . (1+In x)−1

B . (1+In x)−2

C . In x(1+In x)−2

D . None of these

Answer: Option C
:
C

S i n c e, x^{y} = e^{x - y} \Rightarrow y l n x = x - y ∴ y = \frac{x}{1 + I n x} ∴ \frac{d y}{d x} = \frac{l n x}{(1 + I n x)^{2}}

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