Question

If -y^2-2x^3=y, then find d^2y/dx^2 at the point (-1, -2) in simplest form. Explanation honestly not necessary.​

Answer 1

To find d²y/dx², differentiate the given equation twice with respect to x. Plug in the given point (-1, -2) to find the value of d²y/dx².

Step-by-step explanation:

To find d²y/dx², we need to take the second derivative of y with respect to x. To do this, we will differentiate the given equation twice with respect to x.

Starting with the given equation -y²-2x³=y, we differentiate both sides with respect to x to get -2y(dy/dx) - 6x² = dy/dx. This is the first derivative of y with respect to x.

Now, we differentiate the first derivative with respect to x again. Taking the derivative of -2y(dy/dx) - 6x² = dy/dx results in -2(dy/dx)² - 2y(d²y/dx²) - 12x = d²y/dx².

Now, we substitute the given point (-1, -2) into the second derivative equation to get the value of d²y/dx². Plugging in the x-coordinate x = -1 and the y-coordinate y = -2 gives -2(dy/dx)² - 2(-2)(d²y/dx²) - 12(-1) = d²y/dx². Solving for d²y/dx² gives us the answer.