Question

If `sqrt("x"/"y") + sqrt("y"/"x")` = 4, then `"dy"/"dx"` = ____________.

Options

• `(7"y" - "x")/("y" - 7"x")`

• `("y" - 7"x")/(7"x" - "y")`

• `("y" + 7"x")/(7"y" - "x")`

• `(7"x" + "y")/("x" - 7"y")`

Answer 1

If `sqrt("x"/"y") + sqrt("y"/"x")` = 4, then `"dy"/"dx"` = `underline((7"y" - "x")/("y" - 7"x"))`.

Explanation:

We have, `sqrt("x"/"y") + sqrt("y"/"x")` = 4

Squaring both sides, we get

`"x"/"y" + "y"/"x" + 2` = 16

x² + y² = 14xy

On differentiating w.r.t. 'x', we get

`2"x" + 2"y" "dy"/"dx" = 14 ("x" "dy"/"dx" + "y")`

`"x" + "y" "dy"/"dx" = 7"x" "dy"/"dx" + 7"y"`

`"dy"/"dx" ("y" - 7"x") = 7"y" - "x"`

`"dy"/"dx" = (7"y" - "x")/("y" - 7"x")`