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Shtirlitz [24]
2 years ago
7

How do we derive the sum rule in differentiation? (ie. (u+v)' = u' + v')

Mathematics
1 answer:
olganol [36]2 years ago
5 0

It follows from the definition of the derivative and basic properties of arithmetic. Let <em>f(x)</em> and <em>g(x)</em> 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 <em>f(x)</em> + <em>g(x)</em> 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)

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Find <br> 6<br> 2<br> (<br> 9<br> )<br> . Express your answer as a fraction in simplest form.
kotykmax [81]

Based on the expression given, when it is solved, as a fraction in its simplest form it would be 558/1.

<h3>What is the fraction in its simplest form?</h3>

The expression, 62(9) can be rewritten as:

= 62 x 9

This is because the brackets denote that the number within the brackets should be multiplied by the number outside the bracket.

The solution is:

= 62 x 9

= 558

As this is an integer, it means that it has a denominator of 1. The fraction in its simplest form is therefore:

= 558 / 1

Find out more on fractions in their simplest forms at brainly.com/question/18069

#SPJ1

6 0
2 years ago
Pls help me with trig :)
trapecia [35]

Answer:

Step-by-step explanation:

let ∠GEF=x

then ∠GFE=90-x

\frac{GH}{EH}=tan x\\GH=EH~ tan x\\or~ GH=a ~tan x=6 tan x\\\frac{GH}{FH}=tan (90-x)=cot x\\GH=FH*cot x\\GH=b*cot x=27 cot x\\6 tan x=27 cotx\\\frac{tan x}{cot x}=\frac{27}{6}\\tan ^2 x=\frac{27}{6}=\frac{9}{2}\\sec^2x-tan^2x=1\\sec^2 x=1+tan ^2x=1+\frac{9}{2}=\frac{11}{2}\\\frac{EG}{EH}=sec x\\ EG=EH sec x=a sec x= 6 sec x=6\sqrt{\frac{11}{2} } =3\sqrt{22} \approx 14.07

4 0
3 years ago
Find f(-2) f(x)=9x^2-5x+2
borishaifa [10]

Find f(-2) f(x)=9x^2-5x+2


f(-2) means replace x in the equation with -2:


f(-2)=9(-2)^2-5(-2)+2

= 9(4) +10 + 2

= 36 +10 + 2

= 48


f(-2) = 48



4 0
3 years ago
How do you solve this?
BARSIC [14]
7x+2=5(x-2)
7x+2=5x-10
7x-5x=-10-2
2x=-12
x=-6




Regards M.Y.
6 0
2 years ago
A prime factor is a factor that is also a prime number. Create a factor tree for 200 and list the prime factor for 200. Send. He
damaskus [11]

Answer:

Step-by-step explanation:

200 ; 2^3 x 5^2

6 0
3 years ago
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