If x²-y²+3 x-5 y=0 the \;d y/d x is

Correct Answer is : (2x+3)(2y+5)−1(2 x+3)(2 y+5)^{-1}(2x+3)(2y+5)−1

Correct Answer is : (2x+3)(2y+5)−1(2 x+3)(2 y+5)^{-1}(2x+3)(2y+5)−1

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Differential Calculus

Question : 42 of 69

Marks: +1, -0

x^{2}-y^{2}+3 x-5 y=0

\;\frac{d y}{d x}

Solution:

Concept:

Implicit differentiation to find

\frac{dy}{dx}

Explanation:

Given

x^2 - y^2 + 3x - 5y = 0

Differentiate both sides with respect to

x

2x - 2y\frac{dy}{dx} + 3 - 5\frac{dy}{dx} = 0

Group

\frac{dy}{dx}

terms:

-2y\frac{dy}{dx} - 5\frac{dy}{dx} = -2x - 3

Factor:

\frac{dy}{dx}(-2y - 5) = -2x - 3

Multiply both sides by

-1

\frac{dy}{dx}(2y + 5) = 2x + 3

Thus

\frac{dy}{dx} = \frac{2x+3}{2y+5}

Answer:

\frac{dy}{dx} = (2x+3)(2y+5)^{-1}

, which is option A.

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