If f is a differentiable function, find an expression for the derivative of each of the following functions.
(a) y = x2f(x)
(b)
(c)
(d)
(a)
To find: The expression for the derivative of the function
Answer to Problem 48E
The expression for the derivative of the function
Explanation of Solution
Given:
The function is
Derivative rule:
(1) Product Rule:
(2) Quotient Rule: If
(3) Power rule:
(4) Sum rule:
Calculation:
Obtain the derivative of the function
Apply the product rule (1) and the power rule (3) as,
Therefore, the expression for the derivative of the function
(b)
To find: The expression for the derivative of the function
Answer to Problem 48E
The expression for the derivative of the function
Explanation of Solution
Given:
The function is
Calculation:
Obtain the derivative of the function
Apply the quotient rule (2) and the power rule (3) as,
Therefore, the expression for the derivative of the function
(c)
To find: The expression for the derivative of the function
Answer to Problem 48E
The expression for the derivative of the function
Explanation of Solution
Given:
The function is
Calculation:
Obtain the derivative of the function
Apply the quotient rule (2) and the power rule (3) as,
Therefore, the expression for the derivative of the function
(d)
To find: The expression for the derivative of the function
Answer to Problem 48E
The expression for the derivative of the function
Explanation of Solution
Given:
The function is
Calculation:
The given function can be expressed as follows,
Obtain the derivative of the function
Apply the sum rule (4) and the product rule (1) as,
Apply the power rule (3) and simplify the terms,
Simplify the terms and obtain the derivative of the function,
Therefore, the expression for the derivative of the function
Chapter 3 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
Additional Math Textbook Solutions
Calculus: Early Transcendentals (2nd Edition)
Calculus and Its Applications (11th Edition)
University Calculus: Early Transcendentals, Single Variable (3rd Edition)
Glencoe Math Accelerated, Student Edition
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