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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

Calculation of a Function's Domain of Derivative

 Solving Domain Set R (Reals) C (Complex)

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).

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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