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OJEE Leibniz Rule — practice questions

Explore 1 free Leibniz Rule questions in OJEE Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Leibniz Rule questions and exercises with answers

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$\dfrac{d}{dx}\left[\displaystyle\int_0^{x^2} \sin(t^2)\, dt\right] = ?$Read the answer and worked solution →

Worked practice questions

$\dfrac{d}{dx}\left[\displaystyle\int_0^{x^2} \sin(t^2)\, dt\right] = ?$

  1. $\sin(x^4)$
  2. $2x\sin(x^4)$
  3. $\sin(x^2)$
  4. $x^2 \sin(x^2)$
Show answer and solution

Correct answer: B. $2x\sin(x^4)$

**Leibniz rule (FTC + chain):** $\dfrac{d}{dx}\int_0^{u(x)} f(t)dt = f(u(x))\cdot u'(x)$. Here $u = x^2$, $u' = 2x$. **Result:** $\sin(x^4)\cdot 2x$.

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