Recording-2025-04-14T02:47:02.307Z

Understanding Derivatives and Antiderivatives

• You do not need to find the antiderivative when calculating derivatives of integrals.
  • Instead, plug in the limits directly into the function.
• Process:
  1. Find the value of the function at the upper limit.
  2. Subtract the function's value at the lower limit.
  3. Derivative of a constant (after subtraction) is zero, which simplifies calculations.
• This avoids difficulties of finding the antiderivative in complex cases.

The Fundamental Theorem of Calculus

• If you see expressions like g(x) = \int_{g(x)}^{h(x)} f(t) \, dt, to find g':
  1. Use the derivative of an integral rule:
  • g'(x) = f(h(x)) imes h'(x) - f(g(x)) imes g'(x)
  1. Remember the chain rule if there's a function of x as limits.
• For example, if limits are functions