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Part 1: A derivative computation using the chain rule

Suppose $F(x)$ is a differentiable function for all real numbers $x$ . Evaluate the following derivative. Enter the derivative of $F(x)$ using prime notation, i.e., as F'(x).

$\displaystyle{\frac{d}{dx} \left( F(x^{3}) \right) = }$

Part 2: The derivative of a definite integral

Part 3: The derivative of a definite integral and the chain rule