Question

If xe^y = 1, then the value of `dy/dx` at x = 1 is ______.

Options

• −1

• 1

• −e

• `-1/e`

Answer 1

If xe^y = 1, then the value of `dy/dx` at x = 1 is −1.

Explanation:

We have, 

xe^y = 1

Differentiating w.r.t. 'x' both sides

1.e^y + xe^y `dy/dx = 0`

xe^y `dy/dx = -e^y`

`dy/dx = -1/x`

∴ `dy/dx|_(x=1) = -1`