allery$\dfrac{d}{dx}\left[\displaystyle\int_0^{x^2} \sin(t^2)\, dt\right] = ?$
A$\sin(x^4)$
B$2x\sin(x^4)$
C$\sin(x^2)$
D$x^2 \sin(x^2)$
Answer & 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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