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
joja [24]
3 years ago
10

(a) The function k is defined by k(x)=f(x)g(x). Find k′(0).

Mathematics
1 answer:
Brut [27]3 years ago
4 0

Answer:

(a) k'(0) = f'(0)g(0) + f(0)g'(0)

(b) m'(5) = \frac{f'(5)g(5) - f(5)g'(5)}{2g^{2}(5) }

Step-by-step explanation:

(a) Since k(x) is a function of two functions f(x) and g(x) [ k(x)=f(x)g(x) ], so for differentiating k(x) we need to use <u>product rule</u>,i.e., \frac{\mathrm{d} [f(x)\times g(x)]}{\mathrm{d} x}=\frac{\mathrm{d} f(x)}{\mathrm{d} x}\times g(x) + f(x)\times\frac{\mathrm{d} g(x)}{\mathrm{d} x}

this will give <em>k'(x)=f'(x)g(x) + f(x)g'(x)</em>

on substituting the value x=0, we will get the value of k'(0)

{for expressing the value in terms of numbers first we need to know the value of f(0), g(0), f'(0) and g'(0) in terms of numbers}{If f(0)=0 and g(0)=0, and f'(0) and g'(0) exists then k'(0)=0}

(b) m(x) is a function of two functions f(x) and g(x) [ m(x)=\frac{1}{2}\times\frac{f(x)}{g(x)} ]. Since m(x) has a function g(x) in the denominator so we need to use <u>division rule</u> to differentiate m(x). Division rule is as follows : \frac{\mathrm{d} \frac{f(x)}{g(x)}}{\mathrm{d} x}=\frac{\frac{\mathrm{d} f(x)}{\mathrm{d} x}\times g(x) + f(x)\times\frac{\mathrm{d} g(x)}{\mathrm{d} x}}{g^{2}(x)}

this will give <em>m'(x) = \frac{1}{2}\times\frac{f'(x)g(x) - f(x)g'(x)}{g^{2}(x) }</em>

on substituting the value x=5, we will get the value of m'(5).

{for expressing the value in terms of numbers first we need to know the value of f(5), g(5), f'(5) and g'(5) in terms of numbers}

{NOTE : in m(x), g(x) ≠ 0 for all x in domain to make m(x) defined and even m'(x) }

{ NOTE : \frac{\mathrm{d} f(x)}{\mathrm{d} x}=f'(x) }

You might be interested in
1.what is the y-intercept f (x) = 3x+8/x-4?
alekssr [168]

The Eubanks Answer:

Step-by-step explanation:hehus

6 0
3 years ago
Can you help me please ??​
tiny-mole [99]

Answer:

25 pages.

Step-by-step explanation:

all the other answers seem to be less than 200. 20(10) is 200, but it says more than 200 pages. so that means the only correct answer is 25 pages per day. 25(10) is 250 pages, exceeding 200.

3 0
3 years ago
What is the value of the 6 in the number 734,906,257 need fasttt
EastWind [94]

Answer:

6 thousands

Step-by-step explanation:

hope it helps

7 0
2 years ago
Read 2 more answers
Is 3/8 equivalent to 3/8
PIT_PIT [208]
Yes, they're equivalent values.
5 0
3 years ago
Read 2 more answers
1. From 1992 to 2007 the average home price increased by 8% per year. In 1992 Anita Bath
Anuta_ua [19.1K]

Answer:

Anita Bath's home was worth $ 593,195.62 in 2007.

Step-by-step explanation:

Given that from 1992 to 2007 the average home price increased by 8% per year, and in 1992 Anita Bath bought a house for $ 187,000, to determine what was it worth in 2007 the following calculation must be performed:

2007 - 1992 = 15

187000 x 1.08 ^ 15 = X

187000 x 3.172 = X

593,195.62 = X

Therefore, Anita Bath's home was worth $ 593,195.62 in 2007.

5 0
3 years ago
Other questions:
  • of the 125 students in 5th grade, 3/5 of them have a mobile phone. How many students do not have a mobile phone.
    6·2 answers
  • A builder could get 6 sheets of sheetrock for 3$. If he bought 60 sheets , how much money would he have spent
    8·1 answer
  • Factor completely: 10x2 + 2x − 8
    8·2 answers
  • Which number is the least? 2.07, 2.94, 2.81, 2.069
    8·2 answers
  • Need help with question please.
    10·2 answers
  • Y=20(0.5)^x for x=3
    14·1 answer
  • Questions 15 Poge 1 of 1 Tyrone thinks his turtle walks pretty fast compared to other turtles. He wanted to figure out how fast
    10·2 answers
  • A tree is 8 meters tall . what is its height in feet
    10·2 answers
  • Given the following functions f(x) and g(x), solve
    10·1 answer
  • Scott is maling packages. Each small package costs him $2.50 to send. Each large package costs him $4.40. How much will it cost
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!