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Differential Calculus

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Question : 5 of 69

Marks: +1, -0

If

y=\;\frac{11}{(x+1)(x+2)}

\;\frac{dy}{dx}

is

$\;\frac{-11}{(x+1)^{2}(x+2)^{2}}$
$\;\frac{-11(2x+3)}{(x^{2}+3x+2)^{2}}$
11
none

Solution:

Concept:

Use the chain rule to differentiate a rational function.

Explanation:

Let

y = \frac{11}{(x+1)(x+2)} = 11[(x+1)(x+2)]^{-1}

.

Write

u = (x+1)(x+2) = x^2 + 3x + 2

. Then

y = 11 u^{-1}

.

Differentiate:

\frac{dy}{dx} = 11 \cdot (-1) u^{-2} \cdot \frac{du}{dx} = -\frac{11}{u^2} \cdot (2x+3)

.

Substitute back

u

:

\frac{dy}{dx} = -\frac{11(2x+3)}{(x^2+3x+2)^2}

.

Note that

(x^2+3x+2)^2 = (x+1)^2(x+2)^2

, so this matches option B.

Answer:

Option B:

\frac{-11(2x+3)}{(x^{2}+3x+2)^{2}}

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