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Use implicit differentiation to differentiate the equation.?
(3x-2y)^6 = 3y^4 + 9
Please show work/steps along with the answer.
2 Answers
- Anonymous1 decade agoFavorite Answer
Chain rule....
6(3x - 2y)^5(3 - 2(dy/dx)) = 12y³(dy/dx)
18(3x - 2y)^5 - 12(3x - 2y)^5(dy/dx) = 12y³(dy/dx)
18(3x - 2y)^5 = 12y³(dy/dx) + 12(3x - 2y)^5(dy/dx)
18(3x - 2y)^5 = (dy/dx)(12y³ + 12(3x - 2y)^5)
dy/dx = 18(3x - 2y)^5/(12y³ + 12(3x - 2y)^5)
= 18(3x - 2y)^5/(12(y³ + (3x - 2y)^5))
= 3(3x - 2y)^5/(2(y³ + (3x - 2y)^5))
I hope this helps!
Source(s): Knowledge - Ron WLv 71 decade ago
(3x - 2y)^6 = 3y^4 + 9
Differentiate both sides with respect to x:
6(3x - 2y)^5 (3 - 2(dy/dx)) = 12y^3(dy/dx)
Solve for (dy/dx):
18(3x - 2y)^5 - [12(3x - 2y)^5](dy/dx) = 12y^3(dy/dx)
18(3x - 2y)^5 = [12(3x - 2y)^5](dy/dx) + 12y^3(dy/dx)
18(3x - 2y)^5 = [12(3x - 2y)^5 + 12y^3](dy/dx)
[18(3x - 2y)^5] / [12(3x - 2y)^5 + 12y^3] = dy/dx
