Find the derivatives of the given functions. Assume that a,...

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Key Concepts

Derivative

A derivative represents the instantaneous rate of change of a function with respect to a variable. It gives the slope of the tangent line to the function's graph at any specific point and is a fundamental concept in calculus for understanding change.

Power Rule

The power rule is a differentiation method used when dealing with terms of the form x^n. It states that the derivative of x raised to a power n is n times x raised to the (n-1)-th power, simplifying the process of finding derivatives for power functions.

Constant Multiple Rule

The constant multiple rule explains that when a function is multiplied by a constant, the derivative of the entire function is that constant multiplied by the derivative of the function. This rule enables handling constant coefficients during differentiation.

Sum Rule

The sum rule for derivatives indicates that the derivative of a sum of functions is the sum of the derivatives of those individual functions. This rule allows for the straightforward differentiation of functions combined by addition.

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