Find f^'(x) f(x)=a x^3+b x^2+c x+d (a, b, c, d constant) ...

Name: Problem 15, Chapter 2: Calculus Early Transcendentals
Uploaded: 2020-08-13T21:40:31-08:00
Duration: 1 min 51 s
Channel: Paul Teng
Description: Find f^'(x) f(x)=a x^3+b x^2+c x+d (a, b, c, d constant)

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Key Concepts

Derivative

The derivative of a function represents the rate at which the function's value changes with respect to changes in its input. It is a fundamental concept in calculus that formalizes the idea of a slope of the tangent line to the graph of the function at any given point.

Power Rule

The power rule is a basic differentiation rule which states that if a function is given by x raised to a power, x^n, its derivative is n*x^(n-1). This rule is widely used for differentiating polynomial functions.

Constant Multiple Rule

The constant multiple rule in differentiation states that if a function is multiplied by a constant, the derivative of the product is the constant multiplied by the derivative of the function. This property is essential when differentiating terms of a polynomial that include constant coefficients.

Sum Rule

The sum rule for differentiation holds that the derivative of a sum of functions is equal to the sum of their individual derivatives. This rule simplifies the differentiation process for polynomial functions, allowing each term to be differentiated separately.

Constant Function Rule

The constant function rule states that the derivative of a constant is zero. This is used in differentiation of polynomials where constant terms do not contribute to the rate of change.

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