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((x+y)^(2))/(x^(2)-xy+y^(2))

(x+y)2x2−xy+y2 \frac{(x+y)^{2}}{x^{2}-x y+y^{2}}

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Find derivatives of using multiple formulaeright chevron icon

Full solution

Q. (x+y)2x2−xy+y2 \frac{(x+y)^{2}}{x^{2}-x y+y^{2}}
  1. Identify function: Identify the function to differentiate.\newlineFunction: (x+y)2x2−xy+y2\frac{(x+y)^{2}}{x^{2}-xy+y^{2}}
  2. Apply quotient rule: Apply the quotient rule: (v(u′)−u(v′))/v2(v(u') - u(v')) / v^2. Let u=(x+y)2u = (x+y)^2 and v=x2−xy+y2v = x^2 - xy + y^2. u′=u' = derivative of (x+y)2=2(x+y)(1+0)=2(x+y)(x+y)^2 = 2(x+y)(1+0) = 2(x+y). v′=v' = derivative of x2−xy+y2=2x−yx^2 - xy + y^2 = 2x - y.
  3. Substitute into formula: Substitute uu, u′u', vv, and v′v' into the quotient rule formula. (x2−xy+y2)(2(x+y))−(x+y)2(2x−y)(x2−xy+y2)2\frac{(x^2 - xy + y^2)(2(x+y)) - (x+y)^2(2x - y)}{(x^2 - xy + y^2)^2}
  4. Simplify expression: Simplify the expression.\newlineNumerator: (2x3−2x2y+2xy2−2y3−2x3−2xy2+yx2+y3)(2x^3 - 2x^2y + 2xy^2 - 2y^3 - 2x^3 - 2xy^2 + yx^2 + y^3)\newlineDenominator: (x2−xy+y2)2(x^2 - xy + y^2)^2

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