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Domain of Derivative of a Function

Tool to calculate the domain of definition of a function f(x), ie. the set of values x which exists through the derivative f'(x).

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Domain of Derivative of a Function -

Tag(s) : Functions

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Domain of Derivative of a Function

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Calculation of a Function's Domain of Derivative





Tool to calculate the domain of definition of a function f(x), ie. the set of values x which exists through the derivative f'(x).

Answers to Questions

How to calculate the domain of derivative of a function?

Calculating the derivation domain of a function is to calculate the set of definition of its derivative function. Check in \( \mathbb {R} = ] -\infty; +\infty [ \), the values for which the derivative function is not defined. That is, the values of \( x \) such that \( f'(x) \) does not exist.

The calculation of the derivation domain is thus composed of 2 steps:

Step 1: Calculate the derivative of the function

Step 2: Calculate the definition domain of the derivative calculated at step 1

Example: \( f(x) \ln(x) = \log(x) \) is defined over \( \mathbb {R}^{*+} = ] 0 ; +\infty [ \), its derivative is \( f'(x) = \frac{1}{x} \). Which definition domain is \( \mathbb{R}^* = ] -\infty; 0 [ \cup ] 0; +\infty [ \)

What is the domain of derivability of a rational function?

A rational function of the form \( f(x) = \frac{P(x)}{Q(x)} \) has the same definition domain as its derivative. So any rational function is derivable on its own domain of definition.

Indeed, the derivative \( f'(x) = \frac{ P'(x)Q(x) - P(x)Q' }{ Q(x)^2} \) does not modify its domain of definition.

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