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andrey2020 [161]
3 years ago
10

Find the derivative of the function using the definition of derivative.f(x) = mx + qf '(x) =

Mathematics
1 answer:
Natasha_Volkova [10]3 years ago
5 0

Answer:

a) f'(x) = m

b) x \in (-\infty, \infty)

c) x \in (-\infty, \infty)

Step-by-step explanation:

We are given the following in the question:

f(x) = mx + q

a) We have to find the derivative of the given function.

f'(x) = \dfrac{f(x+h)-f(x)}{h}\\\\= \dfrac{m(x+h)+q - mx - q}{h}\\\\f'(x) = \dfrac{mh}{h}\\\\f'(x) = m

b) Domain of f(x)

Domain is the collection of all values of x for which the function is defined.

Domain of f(x) is all real numbers.

x \in (-\infty, \infty)

c) Domain of f'(x)

Domain of f'(x) is all real numbers.

x \in (-\infty, \infty)

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Step-by-step explanation:

We are given the following information in the question:

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where \partial_\xi denotes the partial derivative operator with respect to \xi. Recall that

\vec\imath\times\vec\jmath=\vec k

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