Question

If y=xy x² 1, then when x=-1, dydx is
A. 4/3
B. 3/4
C. -4/3
D. -3/4

Answer 1

The value of dy/dx when x=-1 is -4/3. The correct option is C.

Step-by-step explanation:

To find dy/dx, we need to differentiate the given expression with respect to x. Let's begin:

y = x * y * (x^2 + 1)

Using the product rule, we differentiate y with respect to x:

dy/dx = 1 * y * (x^2 + 1) + x * dy/dx * (x^2 + 1) + x * y * 2x

simplifying further, we get:

dy/dx = y * (x^2 + 1) + x * dy/dx * (x^2 + 1) + 2x^2 * y

Now, substitute the given values x = -1 and y = 1 into the equation:

dy/dx = 1 * (1^2 + 1) + (-1) * dy/dx * (1^2 + 1) + 2(-1)^2 * 1

Simplifying the equation, we have:

dy/dx = 2 - 2dy/dx - 2

3dy/dx = -2

dy/dx = -4/3

Therefore, when x = -1, dy/dx is -4/3.