Find dy/dx by implicit differentiation for the equation x^2 + y^2 = 25.
Answer and explanation
Correct answer: D. -x / y
- Step 1: Differentiate both sides with respect to x: d/dx [x^2 + y^2] = d/dx [25].
- Step 2: 2x + 2y(dy/dx) = 0 implies 2y(dy/dx) = -2x, which simplifies to dy/dx = -x / y.
Answer
-x / y.
Why not the others: 'x / y' misses the negative sign when moving 2x to the right-hand side; '-y / x' inverts the numerator and denominator; 'y / x' has both incorrect sign and inverted fraction.
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