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

Open in App

Solution

$xy = e^{x + y} differentiating both side we get x \frac{dy}{dx} + y = e^{x + y} \times (1 + \frac{dy}{dx}) x \frac{dy}{dx} + y = e^{x + y} + e^{x + y} \frac{dy}{dx} \frac{dy}{dx} (x - e^{x + y}) = e^{x + y} - y \frac{dy}{dx} = \frac{e^{x + y} - y}{(x - e^{x + y})}$

Suggest Corrections

Similar questions

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

Y = \frac{e^{x} - e^{- x}}{e^{x} + e^{- x}}

y = l o g_{e} s i n (e^{x})

3^{x + y} = 81

81^{x - y} = 3^{8}

y_{n}

n

y

n

y_{n} = y_{n + 1}

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

Join BYJU'S Learning Program