Let Calculate the derivative using the product rule. f(x) = and g(x) = which means that f'(x) = and g'(x) = And thus y + (It doesn't matter which part of the sum you enter first or second.) Try checking your answer by multiplying y out and then using power rule. y = √(x² + x³)
Let Calculate the derivative using the product rule. f(x) = and g(x) = which means that f'(x) = and g'(x) = And thus y + (It doesn't matter which part of the sum you enter first or second.) Try checking your answer by multiplying y out and then using power rule. y = √(x² + x³)
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![### Product Rule Derivative Calculation
Let
\[ y = \sqrt[3]{x(x^2 + x^5)} \]
Calculate the derivative using the product rule.
#### Step-by-Step Process:
1. Split the function into parts for the product rule:
\[ f(x) = \]
\[ g(x) = \]
2. Determine the derivatives of these parts:
\[ f'(x) = \]
\[ g'(x) = \]
3. Apply the product rule to find \( y' \):
\[ y' = \]
\[ + \]
(It doesn't matter which part of the sum you enter first or second.)
#### Additional Tip:
Try checking your answer by multiplying \( y \) out and then using the power rule to derive it.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F461e6b03-e26d-48fc-aa6c-204c3b542fc6%2Fa4d9b297-7eb1-4bf6-b0cd-0dd319caecb6%2Fiyxgako_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Product Rule Derivative Calculation
Let
\[ y = \sqrt[3]{x(x^2 + x^5)} \]
Calculate the derivative using the product rule.
#### Step-by-Step Process:
1. Split the function into parts for the product rule:
\[ f(x) = \]
\[ g(x) = \]
2. Determine the derivatives of these parts:
\[ f'(x) = \]
\[ g'(x) = \]
3. Apply the product rule to find \( y' \):
\[ y' = \]
\[ + \]
(It doesn't matter which part of the sum you enter first or second.)
#### Additional Tip:
Try checking your answer by multiplying \( y \) out and then using the power rule to derive it.
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