Ex 25, 9 Verify (i) x3 y3 = (x y) (x2 – xy y2) LHS x3 y3 We know (x y)3 = x3 y3 3xy (x y) So, x3 y3 = (x y)3 – 3xy (x y) = (x y)3 – 3xy (x y) = (x y) (x y)2 – 3xy) Using (ab)2 = a2 b2 2ab = (x y) (x2 y2 2xy) – 3xy = (x y) (x2 y2 – xy) = (x y) (x2 xy y2) = RHS RHS (x y) (x2 – xy y2) Hence proved(xyz)^3 (x y z)(x y z)(x y z) We multiply using the FOIL Method x * x = x^2 x * y = xy x * z = xz y * x = xy y * y = y^2 y * z = yz z * x = xz z * y = yz z * z = z^2 x^3 y^3 z^3 3x^2y 3xy^2 3x^2z 3z^2x 3y^2z 3z^2y 6xyz Lennox Obuong Algebra Student Question How do I plot the equation x^3 y^3 3xy=0 s are words are used to describe and categorize your content Combine multiple words with dashes(),
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(x-y)^(3)=x^(3)-y^(3)-3xy(x-y) =x^(3)-3x^(2)y+3xy^(2)-y^(3)
(x-y)^(3)=x^(3)-y^(3)-3xy(x-y) =x^(3)-3x^(2)y+3xy^(2)-y^(3)-So we set it = 0 i*sqrt(3)(x1) = 0 x1 = 0 x = 1 Then substituting that y = y = y = y = 1 So we end up with all solutions {(x,y) x y = 1} plus the one solution (x,y) = (1,1) Now if you were asking about xy instead of xy, the answer would be xy is always either 1 or 2 Are you sure you didn't make a typo and you were asking about xy and not xy? 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
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#(xy)^3=(xy)(xy)(xy)# Expand the first two brackets #(xy)(xy)=x^2xyxyy^2# #rArr x^2y^22xy# Multiply the result by the last two brackets #(x^2y^22xy)(xy)=x^3x^2yxy^2y^32x^2y2xy^2# #rArr x^3y^33x^2y3xy^2# 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 3SOLUTION 15 Since the equation x 2 xy y 2 = 3 represents an ellipse, the largest and smallest values of y will occur at the highest and lowest points of the ellipse This is where tangent lines to the graph are horizontal, ie, where the first derivative y'=0
Locus of all point $P(x,y)$ satisfying $x^3y^33xy=1$ consists of union of $(A)$a line and an isolated point $(B)$a line pair and an isolated pointPiece of cake Unlock StepbyStep Natural Language Stepbystep explanation we know that A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form or In this problem we have therefore The constant of proportionality is k=3 quarterfreelp and 26 more users found this answer helpful heart outlined Thanks 11
2 92k views Find the maximum and minimum values of x 3 3 x y 2 − 3 x 2 − 3 y 2 4 written 55 years ago by shailymishra30 ♦ 480 • modified 55 years ago Mumbai University > First Year Engineering > Sem 1 > Applied Maths 1 Marks 6 MTranscribed image text Find all the partial derivatives of the first and the second order for f(x, y) = x^2 3xy^2 2y 5 1) Find fx, fy and fxy for e^2x sin (Piy/3) 3) Find fx , fy , and for x^2 y e^xy^4 5) Find fx (x, y) and fy(x, y) for f(x, Y) = xy/x^2y^2 5) Find an equation of the tangent plane to the surface z = 8? If u = x^3 3xy^2 y^3 then ∂^2u/∂y∂x is (a) 3 (b) 6y (c) 6x (d) 2 asked in Applications of Differentiation by Darshee ( 493k points) applications of differentiation
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Click here👆to get an answer to your question ️ If x^3 y^3 = 3axy , find dydx Solve Study Textbooks Join / Login Question If x 3 y 3 = 3 a x y, find d x d y Thay $1=(xy)^3$ vào biểu thức A ta có A=$\frac{(xy)^3}{x^3y^3}\frac{(xy)^3}{xy}=\frac{x^3y^33xy(xy)}{x^3y^3}\frac{x^3y^33xy(xy)}{xy}=1\frac{3xy Find the extreme values of the function x 3 y 3 – 3xy differential calculus;
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Jossaesip62s4 最も共有された X X 3 Y 3 3xy X Y X 3 Y 3 3xy Biết X Y 1
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；X^3y^3=3xy WolframAlpha Volume of a cylinder?Elaborating x 3 y 3 using identity a 3 b 3 = (a b)(a 2 ab b 2) = x ( x y)(x 2 xy y 2) 3xy (x y ) Taking common x( x y ) in both the terms = x ( x y){x 2 xy y 2 3y} ∴ x (x 3 y 3) 3xy ( x y) = x ( x y )(x 2 xy y 2 3y)
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D) 3 x y Solution The answer is D Using identity, (a b) 2 = a 2 b 2 2 a b) = (x y) (3 x y) Hence, one of the factor of given polynomial is 3xy Suggest CorrectionsY^2 at the point a) ( 2, 1, 3), b) ( 0, 1, 7), c) ( 1, ?Factor out the Greatest Common Factor (GCF), '3xy' 3xy(y x) = 0 Ignore the factor 3 Subproblem 1 Set the factor 'xy' equal to zero and attempt to solve Simplifying xy = 0 Solving xy = 0 Move all terms containing x to the left, all other terms to the right Simplifying xy = 0 The solution to this equation could not be determined
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Share It On Facebook Twitter Email 1 Answer 1 vote answered by Taniska (645k points) selected by Vikash Kumar Best answer Let f (x, y) = x 3 y 3 – 3xy Which of the following is a factor of (x y) 3 – (x 3 y 3 )?Consider the function f(x;y) = 3 p x2y Show that the directional derivative exists at the origin (by letting ~u= hcos( );sin( )iand using the de nition), BUT, fis not di erentiable at the origin (because if it were, we could use rf~uto compute D ~uf) SOLUTION Compute the directional derivative at the origin by using the de nition D uf(0;0
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