Further mathematics: Find the derivative of the function x^2 y + (xy)^3 +3x=0 at (-1 , 3)
2 answers:
Answer:
3.
Step-by-step explanation:
Implicit differentiation:
x^2 y + (xy)^3 + 3x = 0
x^2 y + x^3y^3 + 3x = 0
Using the product rule:
2x* y + x^2*dy/dx + 3x^2 y^3 + x^3* (d(y^3)/dx) + 3 = 0
2xy + x^2 dy/dx + 3x^2 y^3 + x^3* 3y^2 dy/dx + 3 = 0
dy/dx(x^2 + 3y^2x^3) = (-2xy - 3x^2y^3 - 3)
dy/dx= (-2xy - 3x^2y^3 - 3) / (x^2 + 3y^2x^3)
At the point (-1, 3).
the derivative = (6 - 81 - 3)/(1 -27)
= -78/-26
= 3.
Step-by-step explanation:
x²y + (xy)³ + 3x = 0
x²y + x³y³ + 3x = 0
Using implicit differentiation and product rule:
2xy + x²(dy/dx) + 3x²y³ + 3y²x³(dy/dx) + 3 = 0
x²(dy/dx) + 3x³y²(dy/dx) = -3x²y³ - 2xy - 3
dy/dx(x²(3xy² + 1)) = -3x²y³ - 2xy - 3
dy/dx = (-3x²y³ - 2xy - 3)/(x²(3xy² + 1))
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