If x³-x y²+y²+2=0 then dy/dx is

Correct Answer is : y2−3x22y(1−x){y²-3x²}{2y(1-x)}2y(1−x)y2−3x2

Correct Answer is : y2−3x22y(1−x){y²-3x²}{2y(1-x)}2y(1−x)y2−3x2

Test Index

Differential Calculus

Question : 51 of 69

Marks: +1, -0

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

\frac{dy}{dx}

Solution:

Concept:

Differentiate the given implicit equation term by term with respect to

x

to find

\frac{dy}{dx}

Explanation:

Given:

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

Differentiate each term:

\frac{d}{dx}(x^{3}) = 3x^{2}

\frac{d}{dx}(-x y^{2}) = -[y^{2} \cdot 1 + x \cdot 2y \frac{dy}{dx}] = -y^{2} - 2xy \frac{dy}{dx}

\frac{d}{dx}(y^{2}) = 2y \frac{dy}{dx}

\frac{d}{dx}(2) = 0

Combine:

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

Group

\frac{dy}{dx}

terms:

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

Factor:

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

Thus

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

Answer:

\frac{y^{2} - 3x^{2}}{2y(1-x)}

, which corresponds to option A.

Go to Question:

Prev Question

Next Question