Question

The value of dy/dx for xy + 4 = 0 at the point (2,-2) is
(A)1
(B) -1
(C) 2
(D) -2​

Answer 1

The value of  $\frac{dy}{dx}$  for  $xy+4=0$ at the point $(2,-2)$ is

(A) 1.

Explanation:

Given:

$xy+4=0$

Point $(2,-2)$

To find:

$\frac{dy}{dx}$  at point $(2,-2)$

Solution:

$xy+4=0$

$xy=-4$

$y=$$\frac{-4}{x}$

Differentiate $x$ on both sides of the equation,

$\frac{dy}{dx}$ $= -4$

$\frac{d}{dx}$ $(x^{-1})$            

Here, use the formula of  ${$ ${\frac{d}{dx} x^{n} =nx^{n-1} }$

Now we get,

$\frac{dy}{dx}=-4 [-1$ × $x^{-1-1}$$]$

$\frac{dy}{dx} =4x^{-2}$

$\frac{dy}{dx}=\frac{4}{x^{2} } }$

$\frac{dy}{dx}$ at point $(2,-2)$ ⇒

$\frac{dy}{dx }$ $= \frac{4}{2^{2} }$

⇒   $\frac{dy}{dx} =1$

So the final answer is 1.

Answer 2

Answer:

(A) 1

Explanation:

See in image.

basically we are differentiating with respect to x and then putting the values