Question

Find $d^{3} y / d x^{3}$.$$y=(2 x-5)^{2}$$.

Name: Problem 35, Chapter 3: Calculus: One Variable
Uploaded: 2021-07-28T10:52:24-08:00
Duration: 1 min 1 s
Channel: Matthys Marthinus
Description: Find d^3 y / d x^3.y=(2 x-5)^2.

   Find $d^{3} y / d x^{3}$.$$y=(2 x-5)^{2}$$.

Calculus: One Variable

Garret J. Etgen,… 10th Edition

Chapter 3, Problem 35

Instant Answer

Solved by Expert Matthys Marthinus

07/28/2021

Step 1

Using the chain rule, we get: \[y' = 2(2x-5) \cdot \frac{d}{dx}(2x-5)\] Show more…

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Find $d^{3} y / d x^{3}$.$$y=(2 x-5)^{2}$$.

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Key Concepts

Higher Order Derivatives

Higher order derivatives are derivatives of derivatives and provide insight into the behavior of a function beyond the rate of change. They can reveal information such as concavity or points of inflection, and in some cases, repeated differentiation results in zero, reflecting the polynomial degree of the original function.

Power Rule

The power rule is a fundamental differentiation rule for functions of the form x^n. It states that the derivative of x^n with respect to x is n*x^(n-1), making it essential for differentiating polynomial expressions efficiently.

Chain Rule

The chain rule is a technique for differentiating composite functions, where one function is applied inside another. It provides a method to differentiate complex functions by taking the derivative of the outer function evaluated at the inner function and multiplying it by the derivative of the inner function.

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