Find the derivative of (6x^2+4y^2)/(3x+7y)=3 using implicit and quotients rule. Thank you!

Answer 1

(6x^2+4y^2)/(3x+7y)=3

we know that (u/v)' = (u'v-uv')/v^2, so

((12x+8yy')(3x+7y)-(6x^2+4y^2)(3+7y'))/(3x+7y)^2 = 0

36x^2 + 84xy + 24xyy' + 56y^2y'-18x^2-12y^2-42x^2y'-28y^2y' = 0
because the denominator is not zero

y'(24x+56y^2-42x^2-28y^2) = 18x^2+12y^2-36x^2-84xy

Now just divide and simplify. check on wolframalpha.com by entering

derivative (6x^2+4y^2)/(3x+7y)=3

Answer 2

Thank you. I appreciate the help.