Find the derivative of the following functions. y=5 x^2+cosx...

Name: Problem 24, Chapter 3: Calculus: Early Transcendentals
Uploaded: 2020-06-12T17:53:15-08:00
Duration: 3 min 47 s
Channel: Theresa Nguyen
Description: Find the derivative of the following functions. y=5 x^2+cosx

Key Concepts

Differentiation

Differentiation is a fundamental concept in calculus that deals with finding the derivative of a function, which represents the instantaneous rate of change or slope of the function at any given point. It is applicable to a wide range of mathematical functions and has numerous applications in physics, engineering, and economics.

Power Rule

The power rule is a basic formula used in differentiation that simplifies the process of finding the derivative of polynomial functions. It states that if a function is of the form x^n, where n is any real number, its derivative is n*x^(n-1), making it particularly useful for functions involving powers of x.

Cosine Derivative

The cosine derivative refers to the specific rule used to differentiate the cosine function. According to this rule, the derivative of cos(x) is -sin(x). This result is essential for handling trigonometric functions and is foundational in the study of calculus.

Constant Multiple Rule

The constant multiple rule is a property of derivatives that allows the constant factor to be pulled out of the differentiation process. This means that when differentiating a constant multiplied by a function, the derivative is that constant multiplied by the derivative of the function, simplifying the differentiation of expressions with constant factors.

Sum Rule

The sum rule is a principle in differentiation which states that the derivative of a sum of functions is equal to the sum of their derivatives. This rule enables the process of differentiating complex functions by breaking them down into simpler parts, each of which can be differentiated individually.

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