Final answer:
The question is not well-defined due to possible typos in the expressions provided for differentiation. If the expressions are correctly written as y = √sin(x) and y = √(4 / x²) + 7, differentiation can proceed after correcting the equation format. However, without proper equations, derivatives cannot be calculated.
Step-by-step explanation:
The question asks us to find the derivative expressed as dx/dy for two different functions involving y. The functions provided are y = √sin x + y and y = √4 / x² + 7. However, these expressions appear to be miswritten or incomplete based on the context provided, and thus cannot be directly differentiated.
If the correct expression for the first function is y = √sin(x) and for the second function y = √(4 / x²) + 7, then we can proceed with the derivatives. However, note that for the first function, as written, y cannot be isolated on one side, and the expression is not explicitly solvable. For the second function, assuming the square root applies only to the 4/x² term, we can proceed as follows:
To find dx/dy for y = √(4 / x²) + 7, first we express y in terms of x: y = √(4 / x²) + 7. Squaring both sides gives us: y² = (4 / x²) + 7. Then we solve this equation for x, and afterward find the derivative of x with respect to y, which is dx/dy. However, we can only solve for x if we isolate the term 4 / x² which implies y - 7 = √(4 / x²), then squaring again (y - 7)² = 4 / x². Cross multiplying gives us 4 = (y - 7)² * x², and solving for x, we would take the square root of the quotient.