Differentiate the function. f(x)=x^3-4 x+6

Name: Problem 7, Chapter 3: Calculus
Uploaded: 2020-03-25T23:16:27-08:00
Duration: 31 s
Channel: Amrita Bhasin
Description: Differentiate the function. f(x)=x^3-4 x+6

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Key Concepts

Differentiation

Differentiation is a fundamental concept in calculus that involves finding the derivative of a function. The derivative represents the instantaneous rate of change of the function with respect to its variable. It is a key tool for understanding how functions behave, particularly in terms of slopes and tangent lines.

Power Rule

The power rule is a basic method in calculus used for differentiating functions of the form x^n, where n is a constant exponent. It states that the derivative of x^n is n multiplied by x raised to the (n-1) power, simplifying the process of finding derivatives of polynomial terms.

Sum Rule

The sum rule states that the derivative of a sum of functions is equal to the sum of the derivatives of those functions. This allows one to differentiate complex functions term by term and is particularly useful when dealing with polynomial expressions.

Constant Rule

The constant rule in differentiation tells us that the derivative of any constant term is zero. This is because constants do not change with respect to the variable, making their rate of change nonexistent.

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