1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Elanso [62]
2 years ago
13

From first principles, find the indicated derivatives​

Mathematics
1 answer:
LenaWriter [7]2 years ago
6 0

By definition of the derivative,

\displaystyle\frac{dr}{ds} = \lim_{h\to0} \frac{\left(\frac{(s + h)^3}2 + 1\right) - \left(\frac{s^3}2 + 1\right)}{h}

\displaystyle\frac{dr}{ds} = \lim_{h\to0} \frac{\left(\frac{s^3+3s^2h+3sh^2+h^3}2 + 1\right) - \left(\frac{s^3}2 + 1\right)}{h}

\displaystyle\frac{dr}{ds} = \lim_{h\to0} \frac{\frac{3s^2h+3sh^2+h^3}2}{h}

\displaystyle\frac{dr}{ds} = \lim_{h\to0} \frac12 \frac{3s^2h+3sh^2+h^3}{h}

\displaystyle\frac{dr}{ds} = \lim_{h\to0} \frac12 (3s^2+3sh+h^2)

\displaystyle\frac{dr}{ds} = \frac{3s^2}2

You might be interested in
A. In a school year the ratio of boys to girls is 3:4. If there are 372 boys, how many girls are there
natima [27]

Answer:

a. 496 girls

b. 110 boys

Step-by-step explanation:

a. 3:4 ------- divide 372 by 3 and you get 124 now multiply that by 4 and you get 496

b. 2:5 -------- divide 275 by 5 and you get 55 now multiply that by 2 and you get 110

7 0
3 years ago
Help pls!! I don’t understand
Debora [2.8K]
\bold{ANSWER:}
x = 55

\bold{SOLUTION:}

7 0
2 years ago
A colored chip is yellow on one side and red on the other. The chip was flipped 50 times and landed yellow side facing up 30 tim
Nat2105 [25]
60% 
50/30 is 0.6
0.6x 100 is 60
7 0
3 years ago
Read 2 more answers
Which of the following best defines an input​
zmey [24]

Answer:

Step-by-step explanation:

A number that goies in and later comes out as an 'output' the output is the result

4 0
3 years ago
Marissa wants to buy a DVD player that runs for at least 150 dollars she already saved $80 and plans to save an additional $10 e
SIZIF [17.4K]
Price of DVD player ≥ $150
Saved = $80
Amount needed = $150 - $80 = $70
Saving per week = $10

Let x be the number of weeks needed:
80 + 10x ≥ 150
10x ≥ 150 - 80
10x ≥ 70
x ≥ 70 ÷ 10 
x ≥ 7

Answer: She needs to save for for at least 7 weeks.

3 0
3 years ago
Other questions:
  • Can someone help me ? I can’t seem to get it :/
    6·1 answer
  • I don't understand the substitution method?
    8·1 answer
  • A potter makes vases and mugs. One day she sold 4 vases and 3 mugs for $80. Another day she sold 3 vases and 6 mugs for $90. How
    11·1 answer
  • Find the solution of y = 2x + 5 for x = 1.
    14·2 answers
  • Help me on this math question please
    13·2 answers
  • A= 1/2 π r ^2 solve for pi
    10·1 answer
  • What is the Range of the data set? 85, 90, 100, 90, 25, 90​
    5·2 answers
  • HELLPPPP PLEASEEE!!
    5·2 answers
  • Which of the following expressions is equal to 6^4
    5·2 answers
  • The product of 4 and a number x
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!