What is a Derivative? Deriving the Power Rule

The video tutorial introduces the concept of differentiation, explaining it as the process of finding the slope of a tangent line to a curve at a given point. It covers the basic understanding of derivatives, illustrating how they represent the rate of change of a function. The tutorial provides examples of calculating derivatives for constant, linear, and quadratic functions, and introduces the power rule, a simplified method for finding derivatives of functions with positive integer exponents.

What is the concept of differentiation and how does it relate to the slope of a tangent line?

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Explain the significance of the derivative of a function at a particular input value.

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How does the derivative of a constant function behave, and why?

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Describe the process of finding the derivative of the function f(x) = x.

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How do you find the derivative of the function f(x) = x^2?

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What pattern can be observed when taking the derivative of polynomial functions?

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What is the power rule in differentiation, and how is it applied?

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