(a) Explanation A differential is a derivative of the function. The derivative of the function f ( x ) is represented as f ′ ( x ) . It is used in various mathematical branches such as statistics, calculus, geometry and differential equations. The derivative of a function f at x is given below: f ′ ( x ) = lim Δ x → 0 f ( x + Δ x ) − f ( x ) Δ x If the degree of the derivative is more than 1, then it is high order derivative such as d 2 x d x 2 , d 3 x d x 3 , … , d n x d x n (b) To determine To explain: The notation for higher-order derivative of the function.

7th Edition

ISBN: 9781524916817

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

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Chapter 3, Problem 6PE

(a)

To determine

To explain: The definition of a higher order derivative of the function.

(b)

To determine

To explain: The notation for higher-order derivative of the function.

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Chapter 3 Solutions

Calculus

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The definition of a higher order derivative of the function.

Solution Summary: The author explains the definition of a higher-order derivative of the function.