Using 💪POWER💪 rule to take derivatives #apcalculus #apcalc #unit2 #shorts

In Topic 2.5 of AP Calculus, we explore the power rule for derivatives, an essential tool for differentiating power functions. This rule provides a straightforward method for finding the derivative of any function in the form x^n.

The process is simple: to differentiate x^n, we bring the exponent n down in front of the term, making it the coefficient, and then subtract 1 from the exponent. If the power function already has a coefficient, the same rule applies. The exponent is brought down to multiply the existing coefficient, and we still subtract 1 from the exponent.

The power rule is equally applicable when the exponent is negative. The negative exponent is brought down to multiply any existing coefficient, and then we subtract 1 from the exponent.

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Unit 2 of AP Calculus is all about Differentiation, including the Definition and Basic Derivative Rules:
2.1 Defining Average and Instantaneous Rates of Change at a Point
2.2 Defining the Derivative of a Function and Using Derivative Notation
2.3 Estimating Derivatives of a Function at a Point
2.4 Connecting Differentiability and Continuity: Determining When Derivatives Do and Do Not Exist
2.5 Applying the Power Rule
2.6 Derivative Rules: Constant, Sum, Difference, and Constant Multiple
2.7 Derivatives of cos(x), sin(x), e^x, and ln(x)
2.8 The Product Rule
2.9 The Quotient Rule
2.10 Finding the Derivatives of Tangent, Cotangent, Secant, and/or Cosecant Functions

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