Evaluating the Derivative of an Inverse Function In Exercises 63-70, verify that f has an inverse function. Then use the function f and the given real number a to find (Hint: See Example 5.)
To prove: The function has an inverse function and calculate .
The value of and
The formula used to calculate derivative of inverse of function is .
Differentiate both sides,
Since, is always negative.
then, is always decreasing and is strictly monotonic on its entire domain.
Hence, is one-one and has an inverse.
Since, is differentiable and has an inverse function
Calculus: Early Transcendental Functions
Calculus: Early Transcendentals
Single Variable Calculus: Early Transcendentals, Volume I
Calculus: An Applied Approach (MindTap Course List)
Finite Mathematics and Applied Calculus (MindTap Course List)
Precalculus: Mathematics for Calculus (Standalone Book)
Essentials of Statistics for The Behavioral Sciences (MindTap Course List)
Essentials Of Statistics
Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach
Calculus (MindTap Course List)
Statistics for The Behavioral Sciences (MindTap Course List)
Understanding Basic Statistics
Single Variable Calculus
Mathematical Applications for the Management, Life, and Social Sciences
Probability and Statistics for Engineering and the Sciences
Mathematical Excursions (MindTap Course List)
Single Variable Calculus: Early Transcendentals
Elementary Geometry For College Students, 7e
Elementary Technical Mathematics
Contemporary Mathematics for Business & Consumers
Elements Of Modern Algebra
Trigonometry (MindTap Course List)
Calculus: Early Transcendental Functions (MindTap Course List)
Calculus of a Single Variable
Finite Mathematics for the Managerial, Life, and Social Sciences
Elementary Geometry for College Students