It follows from the definition of the derivative and basic properties of arithmetic. Let f(x) and g(x) be functions. Their derivatives, if the following limits exist, are

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

The derivative of f(x) + g(x) is then

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

5 0

3 years ago

You and your business partner are mailing advertising flyers to your customers. You address 6 flyers

jonny [76]

Answer:

140

Step-by-step explanation:

3 0

3 years ago

The shoreline of Great Bear Lake is approximately 2719 km (not counting islands). If a map is drawn with a scale of 3 cm:100 km,

bonufazy [111]

Answer:

81.57 cm

Step-by-step explanation:

Given that :

Scale :

3cm : 100km

This means ; 3cm on the map represents an actual length of 100km

Actual length of shoreline = 2719 km

The length of the shoreline on the map will be :

(2719 km / 100 km) * 3cm

27.19 * 3cm

= 81.57 cm

8 0

3 years ago