find the derivative using the limit process of f (x) = – 10x

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find the derivative using the limit process of f (x) = – 10x

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Khải Quang 3 years 2021-08-06T03:56:55+00:00 1 Answers 37 views 0

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  1. thienan
    0
    2021-08-06T03:58:48+00:00
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    Answer:

    \frac{d}{dx} f(x) =-10

    General Formulas and Concepts:

    Calculus

    • Derivative Notation
    • Definition of a Derivative: \lim_{h \to 0} \frac{f(x+h)-f(x)}{h}

    Step-by-step explanation:

    Step 1: Define

    f(x) = -10x

    Step 2: Find Derivative

    1. Substitute:                         \frac{d}{dx} f(x)= \lim_{h \to 0} \frac{-10(x + h)-(-10x)}{h}
    2. Distribute -10:                    \frac{d}{dx} f(x)= \lim_{h \to 0} \frac{-10x -10h-(-10x)}{h}
    3. Distribute -1:                      \frac{d}{dx} f(x)= \lim_{h \to 0} \frac{-10x -10h+10x}{h}
    4. Combine like terms:         \frac{d}{dx} f(x)= \lim_{h \to 0} \frac{-10h}{h}
    5. Divide:                               \frac{d}{dx} f(x)= \lim_{h \to 0} -10
    6. Evaluate:                           \frac{d}{dx} f(x)=-10

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