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KCET2020MathematicsApplication of Derivatives

If y=2 x^ n+1 + 3 x^ n , then x² d^ 2 y d x² is

Options

  1. A6 n(n+1) y
  2. Bn(n+1) y
  3. Cx d y d x +y
  4. Dy

Correct answer

B. n(n+1) y

Step-by-step solution

We have, y aligned y &=2 x^ n+1 + 3 x^ n &=2 x^ n+1 +3 x^ -n ...(i) aligned On differentiating Eq. (i) both sides w.r.t. x , we get d y d x =2(n+1) x^ n +3(-n) x^ -n-1 Again differentiate w.r.t. to x , then we get d² y d x² =2(n+1)(n) x^ n-1 +3(-n)(-n-1) x^ -n-2 =n(n+1) (2 x^ n-1 +3 x^ -n-2 ) x² d² y d x² =n(n+1) (2 x^ n+1 + 3 x^ n ) x² d y d x =n(n+1) y [using Eq. (i)]

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