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Find d y/d x for y=9 (x)/x²
d y/d x=

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Final answer:

The derivative of the function y = 9 + 3x with respect to x, which is denoted as d y/d x, is the slope of the line, which is 3. Since the derivative of a constant is 0 and the derivative of 3x with respect to x is 3, the calculation is straightforward.

Step-by-step explanation:

The question asks for finding the derivative of the function y = 9 + 3x with respect to x, denoted as d y/d x. This function represents a straight line where the y-intercept is 9, and the slope (m) is 3, which corresponds to the coefficient of x in the equation. The derivative of a straight line is simply its slope, since the rate of change of y with respect to x is constant along the entire line.

To find d y/d x, you differentiate both sides of the equation with respect to x. Since the derivative of a constant is 0 and the derivative of 3x with respect to x is 3, the process looks like this:

  1. Start with the function y = 9 + 3x.
  2. Differentiate y with respect to x, leading to d y/d x.
  3. Since the derivative of a constant (9) is 0, it disappears in the derivative.
  4. The derivative of 3x with respect to x is 3.
  5. Therefore, d y/d x for the given function is 3.

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