Question

Find the slope of the tangent line to the curve: √(2x + 9y) + √(2xy) = 9 at the point (8, 1). The slope of the tangent line to the curve at the given point is.

Answer 1

To find the slope of the tangent line to the curve sqrt(2x + 9y) + sqrt(2xy) = 9 at the point (8, 1), find the derivative of the equation and substitute the x-coordinate of the point into the derivative: 161/18.

Step-by-step explanation:

To find the slope of the tangent line to the curve √(2x + 9y) + √(2xy) = 9 at the point (8, 1), we need to find the derivative of the given equation and then substitute the x-coordinate of the point into the derivative. Using the chain rule and simplifying, we find that the derivative is
(1/18x + 9) - (1/18y)
Then we substitute x = 8 and y = 1 into the derivative:
(1/18(8) + 9) - (1/18(1)) = 9 - 1/18 = 161/18