Chapter3: Functions
Section3.5: Transformation Of Functions
Problem 5SE: How can you determine whether a function is odd or even from the formula of the function?
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![**Topic: Using the Definition of the Derivative**
**Learning Objective:** Understand how to find the derivative of a function using the definition of the derivative.
**Problem: Given Functions**
1. Use the definition of the derivative to find the derivative of:
(a) \( f(x) = (x + 1)^2 \)
(b) \( f(x) = \frac{1}{(2x + 3)^2} \)
**Part (a):**
Function: \( f(x) = (x + 1)^2 \)
**Part (b):**
Function: \( f(x) = \frac{1}{(2x + 3)^2} \)
**Method:** To find the derivative of these functions, we will apply the definition of the derivative:
\[ f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h} \]
We will break down the steps for both functions clearly in subsequent examples and practice problems to ensure thorough comprehension.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb1340680-eb9c-48d5-bc71-d4a4fad49dd5%2Fc31f14e0-f84d-41c3-907e-0f100b804da2%2Fb8y70r8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Topic: Using the Definition of the Derivative**
**Learning Objective:** Understand how to find the derivative of a function using the definition of the derivative.
**Problem: Given Functions**
1. Use the definition of the derivative to find the derivative of:
(a) \( f(x) = (x + 1)^2 \)
(b) \( f(x) = \frac{1}{(2x + 3)^2} \)
**Part (a):**
Function: \( f(x) = (x + 1)^2 \)
**Part (b):**
Function: \( f(x) = \frac{1}{(2x + 3)^2} \)
**Method:** To find the derivative of these functions, we will apply the definition of the derivative:
\[ f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h} \]
We will break down the steps for both functions clearly in subsequent examples and practice problems to ensure thorough comprehension.
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