Definite Integral

Step 1: Understanding the Question:
We need to differentiate the given integral function up to the third order. Note that is part of the integrand, so we must separate it before differentiating.

Step 2: Key Formula or Approach:
Use the Leibniz Rule for differentiation under the integral sign:

Step 3: Detailed Explanation:
Rewrite : Differentiating once: Differentiating a second time: Differentiating a third time: Observing that , we substitute:

Step 4: Final Answer:
The correct relation is .