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1 Derivatives of inverse function PROBLEMS and SOLUTIONS (()). (())() 1 () 1 (()) The beauty of this formula is that we don't need to actually determine () to find the value of the derivative at a
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How to fill out derivatives of inverse function
To fill out derivatives of inverse functions, follow these steps:
01
Start by identifying the given function. Let's say the original function is f(x).
02
Find the derivative of the original function, f'(x), using the appropriate derivative rules and techniques.
03
Next, calculate the derivative of the original function with respect to the inverse function, which is denoted as f'(f^(-1)(x)).
04
Now, to fill out the derivatives of the inverse function, you need to use the chain rule. Remember that the derivative of the inverse function with respect to x is equal to 1 divided by the derivative of the original function with respect to the inverse function, or 1/f'(f^(-1)(x)).
05
Simplify the expression obtained in the previous step by substituting the value of f^(-1)(x) with the corresponding value.
In summary, the steps to fill out derivatives of inverse functions are:
01
Identify the given original function, f(x).
02
Find f'(x), the derivative of the original function.
03
Calculate f'(f^(-1)(x)), the derivative of the original function with respect to the inverse function.
04
Apply the chain rule to obtain the derivative of the inverse function.
05
Simplify the expression by substituting the value of f^(-1)(x) with the corresponding value.
Who needs derivatives of inverse functions?
The derivatives of inverse functions are primarily useful in calculus, particularly in optimization problems, curve sketching, and solving equations involving inverse functions. Students studying mathematics, physics, engineering, and other scientific fields often need to work with derivatives of inverse functions to analyze and solve various problems. Additionally, professionals who work in research, data analysis, and modeling may also require the understanding and application of these derivatives in their work.
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What is derivatives of inverse function?
The derivative of an inverse function is the reciprocal of the derivative of the original function.
Who is required to file derivatives of inverse function?
Anyone studying calculus or mathematical analysis may be required to compute derivatives of inverse functions.
How to fill out derivatives of inverse function?
To find the derivative of an inverse function, one can use the formula: (f^-1)'(x) = 1 / f'(f^-1(x)).
What is the purpose of derivatives of inverse function?
The purpose of finding derivatives of inverse functions is to understand the rate of change of the original function when its input is changed.
What information must be reported on derivatives of inverse function?
The values of the original function, its derivative, and the inverse function are typically reported when computing derivatives of inverse functions.
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