Question

If `e^(x^2y)` = c, then `dy/dx` is ______.

Options

• `(xe^(x^2y))/(2y)`

• `(-2y)/x`

• `(2y)/x`

• `x/(2y)`

Answer 1

If `e^(x^2y)` = c, then `dy/dx` is `underlinebb((-2y)/x)`.

Explanation:

Given, `e^(x^2y)` = C

d.w.r to x

`d/dx(e^(x^2y))=d/dx C`

`e^(x^2y) [x^2 dy/dx+y(2x)]=0`

`x^2e^(x^2y) dy/dx+2 xy  e^(x^2y)=0`

`x^2e^(x^2y)  dy/dx= -2xy  e^(x^2y)`

`dy/dx = (-2xye^(x^2y))/(x^2e^(x^2y))`

`dy/dx = (-2y)/x`