If (2x+1)(y+3)=12 then \;dy/dx is

Correct Answer is : 24(2x+1)2\;24/(2x+1)²(2x+1)224

Correct Answer is : 24(2x+1)2\;24/(2x+1)²(2x+1)224

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Differential Calculus

Question : 7 of 69

Marks: +1, -0

(2x+1)(y+3)=12

\;\frac{dy}{dx}

Solution:

Concept:

Implicit differentiation to find

\frac{dy}{dx}

from a given equation.

Explanation:

Given

(2x+1)(y+3)=12

Differentiate both sides with respect to

x

using product rule:

(2x+1)\frac{d}{dx}(y+3) + (y+3)\frac{d}{dx}(2x+1) = 0

Since

\frac{d}{dx}(y+3)=\frac{dy}{dx}

and

\frac{d}{dx}(2x+1)=2

, we get:

(2x+1)\frac{dy}{dx} + (y+3)\cdot 2 = 0

Thus

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

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

From the original equation,

y+3 = \frac{12}{2x+1}

Substitute:

\frac{dy}{dx} = \frac{-2\cdot\frac{12}{2x+1}}{2x+1} = \frac{-24}{(2x+1)^2}

Answer:

\frac{-24}{(2x+1)^2}

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