Compute dy and dy for the given values of x and dx: dx y = x^2 + 6x, x = 5, dx = 0.5

To compute dy for the given function, we start by finding the derivative of the function with respect to x. The function is:

y = x² + 6x

We differentiate y:

dy/dx = 2x + 6

Next, we substitute the value of x = 5 into the derivative:

dy/dx at x = 5:

dy/dx = 2(5) + 6 = 10 + 6 = 16

Now that we have dy/dx, we can compute dy using the formula:

dy = (dy/dx) * dx

Substituting dy/dx and dx:

dy = 16 * 0.5 = 8

In summary:

• dy/dx = 16
• dy = 8