d/dx ≤ft( x+5/(x+1)²(x+2) ) =

Correct Answer is : 3(x+1)2−3(x+2)2−8(x+1)33/(x+1)² - 3/(x+2)² - 8/(x+1)³(x+1)23−(x+2)23−(x+1)38

8/(x+2)² - 3/(x+1)² + 3/(x+1)³

3/(x+1)² - 3/(x+2)² - 8/(x+1)³

3/(x+2)² - 3/(x+1)³ + 8/(x+1)²

8/(x+2)² - 3/(x+1)³ + 3/(x+1)²

Correct Answer is : 3(x+1)2−3(x+2)2−8(x+1)33/(x+1)² - 3/(x+2)² - 8/(x+1)³(x+1)23−(x+2)23−(x+1)38

Test Index

TS EAMCET 5 May 2018 Shift 2 Solved Paper

Section: Mathematics

Question : 19 of 160

Marks: +1, -0

\frac{d}{dx} \left( \frac{x+5}{(x+1)^2(x+2)} \right) =

Solution:

Consider the expression.

\frac{d}{dx} \left( \frac{x+5}{(x+1)^2(x+2)} \right)

Let,

\frac{x+5}{(x+1)^2(x+2)} = \frac{A}{x+1} + \frac{B}{(x+1)^2}

+ \frac{C}{x+2}

Hence,

x+5 = A(x+1)(x+2) + B(x+2)

+ C(x+1)^2

Compare the coefficient of like terms.

A + C = 0

3A + B + 2C = 1

2A + 2B + C = 5

On solving,

A = -3

B = 4

C = 3

Therefore,

\frac{x+5}{(x+1)^2(x+2)} = \frac{-3}{x+1}

+ \frac{4}{(x+1)^2} + \frac{3}{x+2}

Thus,

\frac{d}{dx} \left( \frac{x+5}{(x+1)^2(x+2)} \right)

= \frac{3}{(x+1)^2} - \frac{3}{(x+2)^2} - \frac{8}{(x+1)^3}

Go to Question:

Prev Question

Next Question