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Find (dy)/(dx) if x^(4)+7x+6xy-y^(2)=9

Find dydx \frac{d y}{d x} if x4+7x+6xy−y2=9 x^{4}+7 x+6 x y-y^{2}=9

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Full solution

Q. Find dydx \frac{d y}{d x} if x4+7x+6xy−y2=9 x^{4}+7 x+6 x y-y^{2}=9
  1. Differentiate with respect to xx: First, differentiate both sides of the equation with respect to xx using implicit differentiation.
  2. Rearrange for dydx\frac{dy}{dx}: Rearrange the equation to solve for dydx\frac{dy}{dx}.
  3. Factor out dydx\frac{dy}{dx}: Factor out dydx\frac{dy}{dx} from the terms on the left side.
  4. Solve for dydx\frac{dy}{dx}: Solve for dydx\frac{dy}{dx}.

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