If x² e^{y}+4 x=0 then dy/dx is

Correct Answer is : −ey2x2−4x3ey{-e^{y} 2 x²-4}{x³ e^{y}}x3ey−ey2x2−4

Correct Answer is : −ey2x2−4x3ey{-e^{y} 2 x²-4}{x³ e^{y}}x3ey−ey2x2−4

Test Index

Differential Calculus

Question : 29 of 69

Marks: +1, -0

x^{2} e^{y}+4 \log x=0

\frac{dy}{dx}

Solution:

Concept:

Implicit differentiation with respect to

x

Explanation:

Given:

x^{2} e^{y} + 4 \log x = 0

Differentiate both sides with respect to

x

\frac{d}{dx}(x^{2} e^{y}) + \frac{d}{dx}(4 \log x) = 0

Using product rule:

2x e^{y} + x^{2} e^{y} \frac{dy}{dx} + \frac{4}{x} = 0

Solve for

\frac{dy}{dx}

x^{2} e^{y} \frac{dy}{dx} = -2x e^{y} - \frac{4}{x}

Multiply numerator and denominator:

\frac{dy}{dx} = \frac{-2x e^{y} - \frac{4}{x}}{x^{2} e^{y}} = \frac{-2x^{2} e^{y} - 4}{x^{3} e^{y}}

Thus

\frac{dy}{dx} = \frac{-e^{y} 2 x^{2} - 4}{x^{3} e^{y}}

Answer:

Option C is correct.

Go to Question:

Prev Question

Next Question