Use the table to find the following derivatives. x 1 2 3 4 5 f^'(

Name: Problem 12, Chapter 3: Calculus: Early Transcendentals
Uploaded: 2020-06-08T22:24:21-08:00
Duration: 1 min 3 s
Channel: Anna Waldram
Description: Use the table to find the following derivatives. x 1 2 3 4 5 f^'(x) 3 5 2 1 4 g^'(x) 2 4 3 1 5 .(d)/(d x)(f(x)+g(x))|x=1

step 1 Given this table, we want to find the derivative of f of x plus g of x when x equals 1. So we'll

Question

Use the table to find the following derivatives. $$\begin{array}{cccccc} x & 1 & 2 & 3 & 4 & 5 \\ \hline f^{\prime}(x) & 3 & 5 & 2 & 1 & 4 \\ g^{\prime}(x) & 2 & 4 & 3 & 1 & 5 \end{array}$$ $$\left.\frac{d}{d x}(f(x)+g(x))\right|_{x=1}$$

   Use the table to find the following derivatives.
$$\begin{array}{cccccc}
x & 1 & 2 & 3 & 4 & 5 \\
\hline f^{\prime}(x) & 3 & 5 & 2 & 1 & 4 \\
g^{\prime}(x) & 2 & 4 & 3 & 1 & 5
\end{array}$$
$$\left.\frac{d}{d x}(f(x)+g(x))\right|_{x=1}$$

Calculus: Early Transcendentals

William Briggs, Lyle… 3rd Edition

Chapter 3, Problem 12

Instant Answer

Solved by Expert Anna Waldram

06/08/2020

Step 1

We are asked to find the derivative of the sum of these functions at the point x=1. According to the sum rule in differentiation, the derivative of the sum of two functions is the sum of their derivatives. So, we can write: \[\frac{d}{d x}(f(x)+g(x)) = Show more…

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Use the table to find the following derivatives. $$\begin{array}{cccccc} x & 1 & 2 & 3 & 4 & 5 \\ \hline f^{\prime}(x) & 3 & 5 & 2 & 1 & 4 \\ g^{\prime}(x) & 2 & 4 & 3 & 1 & 5 \end{array}$$ $$\left.\frac{d}{d x}(f(x)+g(x))\right|_{x=1}$$

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Key Concepts

Using Tables for Derivatives

When derivative values are provided in a table, one can directly look up the derivative at a specific input value instead of computing it manually. This method is efficient and practical when working with discrete data or pre-calculated derivative values.

Derivative

A derivative represents the instantaneous rate of change of a function with respect to its variable, quantifying how the function value changes as the input changes. This concept is fundamental in calculus and is used to study the behavior of functions.

Sum Rule

The sum rule in differentiation states that the derivative of the sum of two functions is equal to the sum of the derivatives of those functions. This rule simplifies the differentiation process by allowing one to differentiate each term independently.

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