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MHT CET20243 May 2024Evening ShiftMathematicsDifferentiationActual

Derivative of ^2 x with respect to e ^ x is

Options

  1. A2 x ^2 x e ^ x
  2. B2 x e ^ x
  3. C2 x e ^ x
  4. D-2 x e^ x

Correct answer

D. -2 x e^ x

Step-by-step solution

Let u = ^2 x, v = e ^ x u = ^2 x Differentiating w.r.t. x , we get du ~d x =2 x x Consider, v = e ^ x Differentiating w.r.t. x , we get aligned & dv ~d x =- e ^ x x & d u d v = d u d x d v d x = 2 x x -e^ x x & = -2 x e ^ x aligned

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