Final answer:
The question asks to find the derivative of a function using implicit differentiation. After applying the appropriate rules of differentiation, the derivative (dy/dx) is found to be 2x/√(49 - x²), which corresponds to option B.
Step-by-step explanation:
The question involves finding the derivative of a function using implicit differentiation. When we apply implicit differentiation to the given function, we differentiate both sides of the equation with respect to x. We treat y as a function of x and apply the chain rule where necessary. Let's differentiate the function:
x2 - 49/x2 + 49 = y
We rearrange the equation in order to isolate the y term, which is not required in this case, as we directly differentiate each term with respect to x. For differentiating x2, the result is 2x. Differentiating -49/x2 requires the quotient rule, yielding 98/x3. The derivative of a constant (49) is zero and does not contribute to the derivative. Finally, we apply the chain rule to the y term, resulting in dy/dx. The derivative of the entire equation is then set to zero since y is defined implicitly in terms of x.
2x - 98/x3 + 0 = dy/dx
We solve for dy/dx to find that the derivative of y with respect to x is:
2x/√(49 - x2)
Therefore, the correct answer is option B.