Let $f(x,y) = x^3 y^3 3xy$ We can apply the implicit function theorem here, to solve $y(x)$, in otherwords the equation defines this $y(x)$ implicitly We can solve for $y'$ since this $y(x)$ is differentiable By the chain rule $$\frac {\partial f}{\partial y} = f_y$$ $$y'=\frac{f_x}{f_y}=\frac{3x^23y}{3y^23x}$$ provided that $y\neq \sqrt{x}$Extended Keyboard Examples Upload Random Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals For math, science, nutrition, history, geography, engineering, mathematics, linguistics, sports, finance, musicFind dy/dx x^33xyy^3=3 Differentiate both sides of the equation Differentiate the left side of the equation Tap for more steps Differentiate Tap for more steps By the Sum Rule, the derivative of with respect to is Differentiate using the Power Rule which states that is where
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X(x^3-y^3) 3xy(x-y)-Implicit derivative (dy)/ (dx), x^3y^3=3xy \square!Answer (1 of 3) Differentiate with respect to x 3x^2 3y^2dy/dx=3(xdy/dx y) 3x^23y^2dy/dx =3xdy/dx3y 3y^2dy/dx3xdy/dx=3y3x^2 dy/dx(3y^2–3x)=3y3x^2 dy/dx=(3y
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Ex 25, 9Verify (i) x3 y3 = (x y) (x2 – xy y2)LHS x3 y3We know (x y)3 = x3 y3 3xy (x y)So, x3 y3 = (x y)3 – 3xy (x y) = (x y)3 – 3xyHint if y>0, then y^3< y^32y1< (y1)^3, so the RHS expression cannot be a perfect cube A similar idea works if y is a small enough negative number, but some negative numbers close to 0 (or Find coordinates where the tangent to the curve is horizontalUse implicit differentiation to find the largest yvalue in the loop of the Folium of Descartes, which is given by x3 y3 − 3xy = 0 First, we do the implicit derivative to simplify our equation Because maxima/minima occur when f' (x)=0, we take the implicit derivative and set it equal to 0
F(x)=x³y³3xy f'x=3x²3y=0, 得y=x² f'y=3y²3x=0，代入y得：x^4x=0, 得x=0, 1 得驻点(0, 0) (1, 1) A=f"xx=6x B=f"xy=3 C=f"yy=6y 在(0, 0), A=C=0, B²AC=9>0, 所以这不是极值点；Simplify (3xy^2)^3 (−3xy2)3 ( 3 x y 2) 3 Use the power rule (ab)n = anbn ( a b) n = a n b n to distribute the exponent Tap for more steps Apply the product rule to − 3 x y 2 3 x y 2 ( − 3 x) 3 ( y 2) 3 ( 3 x) 3 ( y 2) 3 Apply the product rule to − 3 x 3 x ( − 3) 3 x 3 ( y 2) 3 ( Explanation differentiate implicitly with respect to x The product rule has to be used on the right side 3x2 3y2 dy dx = 3x dy dx 3y ⇒ 3y2 dy dx −3x dy dx = 3y − 3x2 ⇒ dy dx (3y2 −3x) = 3(y − x2) ⇒ dy dx = 3(y − x2) 3(y2 − x) = y − x2 y2 − x Answer link
Now your easily get the answer X×3 Y×3 = 9×3 5×3 this implies, 27–15=12 Hence 12 is the right answer for this I would suggest a trick for that make a pair in which XY =4 and choose that no if we multiply both then they give less than 45 After 2–3 attempt if you are beginners you can easily find the correct pair for all equationsSolve your math problems using our free math solver with stepbystep solutions Our math solver supports basic math, prealgebra, algebra, trigonometry, calculus and moreWelcome to Sarthaks eConnect A unique platform where students can interact with teachers/experts/students to get
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The two curves `x^(3)3xy^(2)2=0 and 3x^(2)yy^(3)=2`Welcome to Doubtnut Doubtnut is World's Biggest Platform for Video Solutions of Physics, Chemistry, MaBecause maxima/minima occur when f ′(x) = 0, we take the implicit derivative and set it equal to 0 We should end up with a few x3y313xy Final result x3 3xy y3 1 Step by step solution Step 1 Checking for a perfect cube 11 x33xyy31Typo/misspeak around 4 minutes 369=27Multivariable Calculus Find all local maxima/minima and saddle points for the function f(x,y) = x^3 3xy y^3 W
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x(x^3 – y^3) 3xy(x – y) = x(x – y) (x^2 xy y^2) 3xy(x – y) Taking x(x – y) as a common factor;Calculus Find dy/dx x^3y^3=3xy^2 x3 y3 = 3xy2 x 3 y 3 = 3 x y 2 Differentiate both sides of the equation d dx (x3 y3) = d dx (3xy2) d d x ( x 3 y 3) = d d x ( 3 x y 2) Differentiate the left side of the equation Tap for more steps Differentiate= x(x – y) (x^2 xy y^2 3y) = x(x – y) (x^2 xy y^2 3y)
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X 3 y 3 3xy = 1 By using total differentiation concept, \(du = \left( {\frac{{\partial u}}{{\partial x}}} \right)dx \left( {\frac{{\partial u}}{{\partial y}}} \right)dy\) Factorise x(x^3 y^3) 3xy(x y) system of equations step by step solver;Answer (1 of 4) The graph of x^3y^3=3axy is known as the Folium of Descartes It cannot be factored Further, y is not a function of x, because the graph does does not pass the vertical line test An easy way to plot the graph is to take advantage of the fact that the equation is homogeneous
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Factorise x^32x^2y3xy^26y^3 maths polynomials meritnationcom sonia, asked a question subject maths, asked on 6 7 12 if x 3 y 2 3xy x y then log x y 3Calculus Find dy/dx x^3y^3=3x^2y3xy^2 x3 − y3 = 3x2y − 3xy2 x 3 y 3 = 3 x 2 y 3 x y 2 Differentiate both sides of the equation d dx (x3 −y3) = d dx (3x2y−3xy2) d d x ( x 3 y 3) = d d x ( 3 x 2 y 3 x y 2) Differentiate the left side of the equation Tap for more steps DifferentiateSimple and best practice solution for x^3y^33xy=2 equation Check how easy it is, and learn it for the future Our solution is simple, and easy to understand, so
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If u = x log xy where \({x^3} {y^3} 3xy = 1,\) find du/dx SOLUTION F(x, y) = x 3 y 3 3xy – 1 \( \frac{{dy}}{{dx}} = \frac{{\frac{{ \partial f #(x^2y^22xy)(xy)=x^3x^2yxy^2y^32x^2y2xy^2# #rArr x^3y^33x^2y3xy^2# Always expand each term in the bracket by all the other terms in the other brackets, but never multiply two or more terms in the same bracketX^3 y^3 = 3xy^2, find dy/dx using implicit differentiation
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Stack Exchange network consists of 178 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers Visit Stack ExchangeAnswer (1 of 5) At first glance (0,1) and (1,0) are solutions If it has a nice linear solution, fitting this then that would be y= x1, lets plug it in x^3 3x(x1) (x1)^3 1 = x^ 3x^2 3x 1 x^2 3x^2–3x1–1=0 Well, then lets try to factor out yx1 using the usual polynomial divis The derivative is 3 ( y ( x)) 2 y ′ ( x) To differentiate 3 x y ( x), you must remember the product rule The derivative is 3 y ∗ ( x) 3 x y ′ ( x) So in total, differentiation yields 3 x 2 3 y 2 ( x) y ′ ( x) = 3 y ( x) 3 x y ′ ( x) In this form, to find y ′,
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Tính giá trị của biểu thức P=x^3y^33xy biết xy=1 Cho xy=1 Tính giá trị của a) P = x3 y3 3xy P = x 3 y 3 3 x y b) Q = x3 y3 3xy(x2 y2) 6x2y2 (x y) Q = x 3 y 3 3 x y ( x 2 y 2) 6 x 2 y 2 ( x y) Theo dõi Vi phạm Toán 8 Bài 3 Trắc nghiệm Toán 8 Bài 3 Giải bài tập Toán 8 Bài 3Extended Keyboard Examples Upload Random Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals For math, science, nutrition, history, geography, engineering, mathematics, linguistics, sports, finance, musicFirst type the equation 2x3=15 Then type the @ symbol Then type x=6 Try it now 2x3=15 @ x=6 Clickable Demo Try entering 2x3=15 @ x=6 into the text box After you enter the expression, Algebra Calculator will plug x=6 in for the equation 2x3=15 2(6)3 = 15 The calculator prints "True" to let you know that the answer is right More Examples
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求由方程x^3y^33xy=1所确定的隐函数的导数 为什么x^3y^3xy=0的隐函数的二阶导数在第一次求导 更多类似问题 >To ask Unlimited Maths doubts download Doubtnut from https//googl/9WZjCW `(x^33xy^2)dx=(y^33x^2y)dy`Get stepbystep solutions from expert tutors as fast as 1530 minutes Your first 5 questions are on us!
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Transcribed image text Find the critical points of f(x, y) = x^3 y^3 3xy and test for local max or min or saddle Contour lines are drawn at the right at intervals of z = 1 Your task now is to find the global MAX and MIN points of the function f(x, y) on the circle x^2 y^2 lessthanorequalto 4 Use the contour diagram to identify (graphically the maximum and minimum pointsFactor x^3y^3 x3 − y3 x 3 y 3 Since both terms are perfect cubes, factor using the difference of cubes formula, a3 −b3 = (a−b)(a2 abb2) a 3 b 3 = ( a b) ( a 2 a b b 2) where a = x a = x and b = y b = y (x−y)(x2 xyy2) ( x y) ( x 2 x y y 2) Correct answer (Xy)^3=x^3y^33xy(xy) Brady has a year fixed rate mortgage for $215,500 with monthly payments of 1,305the annual interest rate is 4% what is the total cost of the principal and interest for this loan rounded to the nearest dollar
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Experts are tested by Chegg as specialists in their subject area We review their content and use your feedback to keep the quality high 100% (9 ratings)Find and classify all critical points of the function f(x,y)= 4−x 3 y 3 −3xy Expert Answer Who are the experts? Explanation y3 x3 = 3xy 3y2 dy dx 3x2 = 3(x dy dx y ⋅ 1) (Inplicit differentiation, Power rule and Product rule) 3(y2 −x) dy dx = 3(y − x2) Multiply through by ( − 1 3) → (x −y2) dy dx = (x2 − y) dy dx = x2 −y x −y2 Answer link
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Free PreAlgebra, Algebra, Trigonometry, Calculus, Geometry, Statistics and Chemistry calculators stepbystep Factorize x(x^3y^3) 3xy (xy) asked in Mathematics by Sonu khan (356k points) factorisation of algebraic expressions;Show, by left side, that $$\frac{x^3y^3}{xy} = x^2xyy^2,$$ or $$\frac{x^3y^3}{x^2xyy^2} = xy$$ You may read about "Long Division of Polynomials" See also LINK for knowing the process
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Hello students, today we are going to learn algebraic identities (XY)^3 = X^3 3XY (XY) Y^3 (XY)^3 = X^3 3XY (XY) Y^3#algebraicidentities #ma We have (x3 y3) = 3xy2 dy dx We can rearrange this Differential Equation as follows 3 dy dx = x3 y3 xy2 = x3 xy2 y3 xy2 = x2 y2 y x = ( x y)2 y x This would lead us to try a substitution, Let v = y x ⇒ y = vx⇒ x 3 y 3 = (x y) 3 − 3 x y (x y) = 3 3 − 3 ⋅ 3 ⋅ 3 = 0 This is interesting because the final solution involves only Real numbers, but the intermediate values of x
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Answer (1 of 2) Making this equation in the form y = f(x) is tough way to solve the problem According to me, it is better to differentiate the whole equation wrt x and then separate the dy/dx term to the LHS and other to RHS Sol x^3y^33xy^2=8 diff Stack Exchange network consists of 178 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers Visit Stack ExchangeSolve your math problems using our free math solver with stepbystep solutions Our math solver supports basic math, prealgebra, algebra, trigonometry, calculus and more
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