Write the composite function in the form f(g(x)). [Identify the inner function u = g(x) and the outer function y = f(u).] Then find the derivative dy/dx.
y = sin( cot x)
To find: The composite function in the form
Answer to Problem 4E
The inner function is
The derivative of y is
Explanation of Solution
Given:
The function is
Formula used:
The Chain Rule:
If h is differentiable at x and g is differentiable at
Calculation:
Let the inner function be
Then,
Therefore,
Hence, the inner function is
Thus, the required form of composite function is
Obtain the derivative of y is
Let
Apply the chain rule as shown in equation (1),
The derivative
Substitute
The derivative
The derivative of
Thus, the derivative of
Substitute
Therefore, the derivative of
Chapter 3 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
Additional Math Textbook Solutions
University Calculus
Calculus, Single Variable: Early Transcendentals (3rd Edition)
Precalculus: Mathematics for Calculus - 6th Edition
Calculus: Early Transcendentals (2nd Edition)
Calculus: Single And Multivariable
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