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KCET2021MathematicsDifferentiation

If y=(x-1)²(x-2)³(x-3)⁵ , then d y d x at x=4 is equal to

Options

  1. A108
  2. B54
  3. C36
  4. D516

Correct answer

D. 516

Step-by-step solution

y=(x-1)²(x-2)³(x-3)⁵ Taking log on both sides, aligned & y= [(x-1)²(x-2)³(x-3)⁵ ] & y=2 (x-1)+3 (x-2)+5 (x-3) aligned On both sides differentiating w.r.t. x , we get 1 y d y d x = 2 x-1 + 3 x-2 + 5 x-3 d y d x =(x-1)²(x-2)³(x-3)⁵ [ 2 (x-1) + 3 (x-2) + 5 (x-3) ] ( d y d x )_ x=4 =3² 2³ 1⁵ [ 2 3 + 3 2 +5 ]=9 8 ( 4+9+30 6 )=516

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