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99 Percentile Qs Bank for JEE MainMathematicsDifferentiation

d d x ( x+5 (x+1)^2(x+2) )=

Options

  1. A8 (x+2)^2 - 3 (x+1)^2 + 3 (x+1)^3
  2. B3 (x+1)^2 - 3 (x+2)^2 - 8 (x+1)^3
  3. C3 (x+2)^2 - 3 (x+1)^3 - 8 (x+1)^2
  4. D8 (x+2)^2 - 3 (x+1)^3 + 3 (x+1)^2

Correct answer

B. 3 (x+1)^2 - 3 (x+2)^2 - 8 (x+1)^3

Step-by-step solution

Let x+5 (x+1)^2(x+4) = A (x+1) + B (x+1)^2 + C (x+4) aligned & x+5=A(x+1)(x+2)+B(x+2)+c(x+1)^2 & x+5=x^2(A+C)+x(3 A+B+2 C)+2 A+2 B+C . aligned On comparing the coefficients of like power of x , we get aligned A+C & =0, 3 A+B+2 C & =1 and 2 A+2 B+C=5 aligned On substituting A=-C in last two equations, we get aligned B-C & =1 2 B-C & =5 aligned and 2 B-C=5 On subtracting Eqs. (ii) and (iii), we get B=4 C=3 [from Eq. (ii)] and hence A=-3 Now, (x+5) (x+1)^2(x+2) = -3 (x+1) + 4 (x+1)^2 + 3 (x+2) On differentiating both

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