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joja [24]
2 years ago
10

Derivative using direct definition of derivative 2-x/2+x

Mathematics
1 answer:
Daniel [21]2 years ago
3 0

Let <em>f(x)</em> = (2 - <em>x</em>)/(2 + <em>x</em>). By definition of the derivative,

\displaystyle f'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}h

\displaystyle f'(x)=\lim_{h\to0}\frac{\frac{2-(x+h)}{2+(x+h)}-\frac{2-x}{2+x}}h

\displaystyle f'(x)=\lim_{h\to0}\frac{\frac{(2-x-h)(2+x)-(2-x)(2+x+h)}{(2+x+h)(2+x)}}h

\displaystyle f'(x)=\lim_{h\to0}\frac{-4h}{h(2+x+h)(2+x)}

\displaystyle f'(x)=-4\lim_{h\to0}\frac1{(2+x+h)(2+x)}=\boxed{-\frac4{(2+x)^2}}

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Step-by-step explanation:

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Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
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Answer:

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remember that local minimuns are points in which the function was decreasing and starts increasing.

you can try two ways of doing it, graphing the functions or using derivatives.

since this are twelve functios the easier way is to graph them.

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5 0
1 year ago
Read 2 more answers
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