To calculate: The second derivative of the function
Answer to Problem 31E
The second derivative of the function is
Explanation of Solution
Given information:
The function
Formula used:
The chain rule for differentiation is if f is a function of g then
Power rule for differentiation is
Calculation:
Consider the function
Differentiate both sides with respect to x ,
Recall that power rule for differentiation is
Apply it. Also observe that y is a function of x,
Isolate the value of
Therefore, the value of first derivative of the function is
Now, again differentiate the above expression with respect to x . Recall that quotient rule for differentiation is
Apply it. Also observe that y is a function of x,
Now, substitute the value
According to the question
Thus, the second derivative of the function is
Chapter 3 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition