Westonci.ca makes finding answers easy, with a community of experts ready to provide you with the information you seek. Explore a wealth of knowledge from professionals across various disciplines on our comprehensive Q&A platform. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.
Sagot :
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))
[tex]{ (\frac{dy}{dx})}^{ - 1} _{3} = \frac{( - 3{( - 1)}^{2} ({3})^{3} - 2( - 1)(3) - 3) }{({( - 1)}^{2}(3( - 1){(3)}^{2} + 1)} \\ \\ { (\frac{dy}{dx})}^{ - 1} _{3} = \frac{( -81 + 6 - 3)}{( - 27 + 1)} \: \\ \\ { (\frac{dy}{dx})}^{ - 1} _{3} = \frac{ - 78}{ - 26} \\ \\ { (\frac{dy}{dx})}^{ - 1} _{3} = 3[/tex]
We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.