Question

Please help on implicit differentiation problem.

Answer 1

Answer:

$\frac{ d^{2} y}{dx^{2} } = -10$

Step-by-step explanation:

Concept : We have to differentiate the given equation twice and then put the values of x and y at the given point.

The given point is (2,-5).

Given    xy - y = -5

Differentiating both sides,

$x \times \frac{dy}{dx} + y - \frac{dy}{dx}$ = 0

Substitute (x,y) as (2,-5)

$2 \times \frac{dy}{dx} -5 - \frac{dy}{dx}$ = 0

$\frac{dy}{dx} = 5$

Differentiating again, we get

$\frac{dy}{dx} + x \times \frac{ d^{2} y}{dx^{2} } + \frac{dy}{dx} - \frac{ d^{2} y}{dx^{2} } = 0$

Substitute values of x , y and \frac{dy}{dx} ,

$5 + 2 \times \frac{ d^{2} y}{dx^{2} } + 5 - \frac{ d^{2} y}{dx^{2} } = 0$

$\frac{ d^{2} y}{dx^{2} } = -10$