Find the following using the table below. X 1 2 3 4 3 4 f(x) 2 1 f'(x) 2 4 3 1 g(x) 2 4 3 1 g'(x) 2 4 3 1 h'(4) if h(x) = f(x) ·g(x) || h'(4) if h(x): = f(x) g(x) Enter a mathematical expression [more..] Question Help: Message instructor
Find the following using the table below. X 1 2 3 4 3 4 f(x) 2 1 f'(x) 2 4 3 1 g(x) 2 4 3 1 g'(x) 2 4 3 1 h'(4) if h(x) = f(x) ·g(x) || h'(4) if h(x): = f(x) g(x) Enter a mathematical expression [more..] Question Help: Message instructor
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![The problem involves finding derivatives using a table of values for functions \( f(x) \) and \( g(x) \).
Below is the table provided for evaluating the functions:
\[
\begin{array}{c|cccc}
x & 1 & 2 & 3 & 4 \\
\hline
f(x) & 2 & 1 & 3 & 4 \\
f'(x) & 2 & 4 & 3 & 1 \\
g(x) & 2 & 4 & 3 & 1 \\
g'(x) & 2 & 4 & 3 & 1 \\
\end{array}
\]
The tasks are:
1. Calculate \( h'(4) \) if \( h(x) = f(x) \cdot g(x) \).
2. Calculate \( h'(4) \) if \( h(x) = \frac{f(x)}{g(x)} \).
For each part, the student needs to use derivatives and the values from the table.
For product rule:
\[
h'(x) = f'(x)g(x) + f(x)g'(x)
\]
For quotient rule:
\[
h'(x) = \frac{f'(x)g(x) - f(x)g'(x)}{(g(x))^2}
\]
These formulas will be applied using the values at \( x = 4 \) from the table.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5963b474-a441-468b-8c4e-b34b2e3806b1%2F73a4101f-df2e-4e34-b3f6-b6cdd97ed628%2Fnpo2uju_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The problem involves finding derivatives using a table of values for functions \( f(x) \) and \( g(x) \).
Below is the table provided for evaluating the functions:
\[
\begin{array}{c|cccc}
x & 1 & 2 & 3 & 4 \\
\hline
f(x) & 2 & 1 & 3 & 4 \\
f'(x) & 2 & 4 & 3 & 1 \\
g(x) & 2 & 4 & 3 & 1 \\
g'(x) & 2 & 4 & 3 & 1 \\
\end{array}
\]
The tasks are:
1. Calculate \( h'(4) \) if \( h(x) = f(x) \cdot g(x) \).
2. Calculate \( h'(4) \) if \( h(x) = \frac{f(x)}{g(x)} \).
For each part, the student needs to use derivatives and the values from the table.
For product rule:
\[
h'(x) = f'(x)g(x) + f(x)g'(x)
\]
For quotient rule:
\[
h'(x) = \frac{f'(x)g(x) - f(x)g'(x)}{(g(x))^2}
\]
These formulas will be applied using the values at \( x = 4 \) from the table.
Expert Solution
Step 1: Step 1
1) given function h(x)=f(x).g(x)
Derivative w.r.t 'x' by using the product rule
formula of the product rule
d/dx[f(x)g(x)]=[(d/dx)f(x)]g(x)+f(x)[(d/dx)g(x)]
h′(x)=f(x)×g′(x)+g(x)×f′(x)
put x=4 in above equation
f′(4)=1
f′(4)=1
g(4)=1
g′(4)=1
h′(4)=4×1+1×1
h'(4)=5
Step by step
Solved in 3 steps
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