If 3 y²-2 x y-x=0, then the value of d y/d x at y=2 is...

Correct Answer is : 253625/363625

Correct Answer is : 253625/363625

Test Index

MHTCET 19 Apr 2026 Shift 2 Paper

Question : 124 of 150

Marks: +1, -0

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

\frac{d y}{d x}

y=2

is...

Solution:

Concept:

Use implicit differentiation to find

\frac{dy}{dx}

from the given relation between

x

and

y

Explanation:

Given equation:

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

Substitute

y = 2

to find the corresponding value of

x

3(2)^{2} - 2x(2) - x = 0

12 - 4x - x = 0

12 - 5x = 0

x = \frac{12}{5}

Differentiate the given equation implicitly with respect to

x

6y \frac{dy}{dx} - 2\left(x \frac{dy}{dx} + y\right) - 1 = 0

(6y - 2x) \frac{dy}{dx} = 2y + 1

\frac{dy}{dx} = \frac{2y + 1}{6y - 2x}

Now substitute

y = 2

and

x = \frac{12}{5}

\frac{dy}{dx} = \frac{2(2) + 1}{6(2) - 2\left(\frac{12}{5}\right)}

= \frac{5}{12 - \frac{24}{5}} = \frac{5}{\frac{36}{5}} = \frac{25}{36}

Answer:

The value of

\frac{dy}{dx}

y = 2

\frac{25}{36}

, i.e. Option C.

Go to Question:

Prev Question

Next Question