1), let x = 1 and y = 1:dy/dx = [ -18(1)^2 - 14(1)(1) - 6(1)^2 ] / [ 7(1)^2 + 12(1)(1) + 30(1)^2 ] --> Simplify.ANSWER:dy/dx = -38 / 49 Hope that helps!-6x^3 + 7x²y + 6xy² + 10y^3 = 29Lets find the derivative dy/dx18x² + (14xy + 7x²dy/dx) + (6y² + 12xydy/dx) + 30y²dy/dx = 0dy/dx = (-18x² - 14xy - 6y²)/(7x² + 12xy + 30y²)At (1 ,......
y' = (-18 - 14 - 6)/(7 + 12 + 30)
y' = -38/49
so the slope is -38/49
Take the derivative.
Notes: Recall d/dx [ y ] = dy/dx. Also, if you see xy together, you must perform the product rule.
6x^3 + 7(x^2)y + 6x(y^2) + 10y^3 = 29 --> Take the derivative.
18x^2 + 14xy + 7(x^2)(dy/dx) + 6y^2 + 6x(2y)(dy/dx) + 30(y^2)(dy/dx) = 0 --> Rewrite and simplify.
18x^2 + 14xy + 7(x^2)(dy/dx) + 6y^2 + 12xy(dy/dx) + 30(y^2)(dy/dx)= 0 --> Subtract 18x^2, 14xy, and 6y^2 from both sides.
7(x^2)(dy/dx) + 12xy(dy/dx) + 30(y^2)(dy/dx) = -18x^2 - 14xy - 6y^2 --> Factor out a common (dy/dx).
(dy/dx) [ 7x^2 + 12xy + 30y^2 ] = -18x^2 - 14xy - 6y^2 --> Divide through by 7x^2 + 12xy + 30y^2.
dy/dx = [ -18x^2 - 14xy - 6y^2 ] / [ 7x^2 + 12xy + 30y^2 ]
Substitute the point (1, 1), let x = 1 and y = 1:
dy/dx = [ -18(1)^2 - 14(1)(1) - 6(1)^2 ] / [ 7(1)^2 + 12(1)(1) + 30(1)^2 ] --> Simplify.
ANSWER: dy/dx = -38 / 49
Hope that helps!