(a)
To State: The derivative of
(a)
Answer to Problem 2RCC
The derivative of
Explanation of Solution
Binomial expansion:
Calculation:
Obtain the derivative of y.
Therefore, the derivative of y is
(b)
To find: The derivative of
(b)
Answer to Problem 2RCC
The derivative of
Explanation of Solution
Calculation:
Obtain the derivative of y.
Use
Therefore, the derivative of y is,
(c)
To find: The derivative of
(c)
Answer to Problem 2RCC
The derivative of y is,
Explanation of Solution
Calculation:
Obtain the derivative of y.
Since
Therefore, the derivative of y is
(d)
To find: The derivative of
(d)
Answer to Problem 2RCC
The derivative of
Explanation of Solution
Result used:
The value
Calculation:
Obtain the derivative of y.
Use
Let
Use the result stated above,
Therefore, the derivative of y is
(e)
To find: The derivative of
(e)
Answer to Problem 2RCC
The derivative of
Explanation of Solution
Calculation:
Obtain the derivative of y.
Therefore, the derivative of y is
(f)
To find: The derivative of
(f)
Answer to Problem 2RCC
The derivative of y is,
Explanation of Solution
Calculation:
Obtain the derivative of y.
Simplify further,
Therefore, the derivative of y is
(g)
To find: The derivative of
(g)
Answer to Problem 2RCC
The derivative of y is
Explanation of Solution
Calculation:
Obtain the derivative of y.
Simplify further,
Therefore, the derivative of y is
(h)
To find: The derivative of
(h)
Answer to Problem 2RCC
The derivative of y is
Explanation of Solution
Calculation:
Obtain the derivative of y.
Simplify further,
Therefore, the derivative of y is
(i)
To find: The derivative of
(i)
Answer to Problem 2RCC
The derivative of y is
Explanation of Solution
Calculation:
Obtain the derivative of y.
Simplify further,
That is,
Therefore, the derivative of y is
(j)
To find: The derivative of
(j)
Answer to Problem 2RCC
The derivative of y is
Explanation of Solution
Calculation:
Obtain the derivative of y.
Simplify further,
That is,
Therefore, the derivative of y is,
(k)
To find: The derivative of
(k)
Answer to Problem 2RCC
The derivative of y is
Explanation of Solution
Calculation:
Obtain the derivative of y.
Simplify further,
Apply the limit,
Therefore, the derivative of y is
(l)
To find: The derivative of
(l)
Answer to Problem 2RCC
The derivative of y is
Explanation of Solution
Calculation:
Consider the function
That is
Differentiate implicitly with respect x,
Since
Substitute
Therefore, the derivative of y is
(m)
To find: The derivative of
(m)
Answer to Problem 2RCC
The derivative of y is
Explanation of Solution
Calculation:
Consider the function
That is
Differentiate implicitly with respect x,
Since
Substitute
Therefore, the derivative of y is
(n)
To find: The derivative of
(n)
Answer to Problem 2RCC
The derivative of y is
Explanation of Solution
Calculation:
Consider the function
That is,
Differentiate implicitly with respect x,
Therefore, the derivative of y is
(o)
To find: The derivative of
(o)
Answer to Problem 2RCC
The derivative of y is
Explanation of Solution
Calculation:
Obtain the derivative of y.
Therefore, the derivative of y is
(p)
To find: The derivative of
(p)
Answer to Problem 2RCC
The derivative of y is
Explanation of Solution
Calculation:
Obtain the derivative of y.
Therefore, the derivative of y is
(q)
To find: The derivative of
(q)
Answer to Problem 2RCC
The derivative of y is
Explanation of Solution
Calculation:
Obtain the derivative of y.
Simplify further,
Therefore, the derivative of y is
(r)
To find: The derivative of
(r)
Answer to Problem 2RCC
The derivative of y is
Explanation of Solution
Calculation:
Consider the function
That is,
Simplify further,
Solve the above quadric equation,
That is
Obtain the derivative
Simplify in terms and obtain the derivative,
Therefore, the derivative of y is
(s)
To find: The derivative of
(s)
Answer to Problem 2RCC
The derivative of y is
Explanation of Solution
Calculation:
Consider the function
That is,
Simplify further,
Solve the above quadric equation,
That is,
Obtain the derivative
Simplify in terms and obtain the derivative,
Therefore, the derivative of y is
(t)
To find: The derivative of
(t)
Answer to Problem 2RCC
The derivative of y is
Explanation of Solution
Calculation:
Consider the function
That is,
Simplify further,
Take natural logarithm on both sides,
That is,
Obtain the derivative
Therefore, the derivative of y is
Chapter 3 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
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