Question

Determine d²y/dx² when 4x² + 3y² = 4 a) 0 b) -24x / (4x² + 3y²) ³/² c) 24x / (4x² + 3y²) ³/² d) -24x / (4x² + 3y²) ⁵/²

Answer 1

Second derivative d²y/dx² is found by performing implicit differentiation twice on the equation 4x² + 3y² = 4. The correct answer is d) -24x / (4x² + 3y²) ³/².

Step-by-step explanation:

The student is asking for the second derivative of the function defined implicitly by the equation 4x² + 3y² = 4. To find the second derivative d²y/dx², we first need to find the first derivative using implicit differentiation.

After obtaining dy/dx, we differentiate it one more time with respect to x while applying the chain rule for derivatives.

Here are the steps:

1. Differentiate the given equation implicitly with respect to x to find dy/dx.
2. Once dy/dx is found, differentiate it again with respect to x to find d²y/dx².
3. Simplify the expression for d²y/dx² and match it with the given options.

Through the calculations, the correct answer should be b) -24x / (4x² + 3y²) ³/².