If y = x + 3/2x+1 then dy/dx is

Correct Answer is : 4x2+2x−5(2x+1)24x²+2x-5/(2x+1)²(2x+1)24x2+2x−5

Correct Answer is : 4x2+2x−5(2x+1)24x²+2x-5/(2x+1)²(2x+1)24x2+2x−5

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Differential Calculus

Question : 4 of 69

Marks: +1, -0

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

\frac{dy}{dx}

Solution:

Concept:

Differentiate term by term using power rule and chain rule.

Explanation:

Given

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

Differentiate:

\frac{dy}{dx} = \frac{d}{dx}(x) + \frac{d}{dx}\left(\frac{3}{2x+1}\right)

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

Write

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

Derivative:

3 \cdot (-1)(2x+1)^{-2} \cdot 2 = -6(2x+1)^{-2} = -\frac{6}{(2x+1)^2}

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

Answer:

1 - \frac{6}{(2x+1)^2}

, which corresponds to option B.

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