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
liubo4ka [24]
3 years ago
14

Finding Higher-Order Derivatives In Exercise, find the second derivative of the function.

Mathematics
1 answer:
Vinvika [58]3 years ago
3 0

Answer: The second derivative of the function is f''(x)=\dfrac{1}{2x}

Step-by-step explanation:

Since we have given that

f(x)=x\ln \sqrt{x}+2x

We need to find the second derivative of the function.

So, the first derivative would be

f'(x)=1\times \ln\sqrt{x}+x\dfrac{1}{\sqrt{x}}\times \dfrac{1}{2\sqrt{x}}+2\\\\f'(x)=\ln \sqrt{x}+\dfrac{1}{2}+2\\\\f'(x)=\ln\sqrt{x}+\dfrac{3}{2}

Now, second derivative would be

f''(x)=\dfrac{1}{\sqrt{x}}\times \dfrac{1}{2\sqrt{x}}\\\\f''(x)=\dfrac{1}{2x}

Hence, the second derivative of the function is f''(x)=\dfrac{1}{2x}

You might be interested in
If O is an angle in standard position and its terminal side passes through the point
Nataliya [291]

Answer:

-1/3

Step-by-step explanation:

6 0
2 years ago
Let g(x) = 2x and h(x)= x^2 -4. find (g o h)(0)
finlep [7]
The answer is -8

====================================================

Explanation:

There are two ways to get this answer

Method 1 will have us plug x = 0 into h(x) to get
h(x) = x^2 - 4
h(0) = 0^2 - 4
h(0) = 0 - 4
h(0) = -4
Then this output is plugged into g(x) to get
g(x) = 2x
g(-4) = 2*(-4)
g(-4) = -8 which is the answer
This works because (g o h)(0) is the same as g(h(0)). Note how h(0) is replaced with -4
So effectively g(h(0)) = -8 which is the same as (g o h)(0) = -8

-----------------------

The second method involves a bit algebra first
Start with the outer function g(x). Then replace every x with h(x). On the right side, we will replace h(x) with x^2-4 because h(x) = x^2-4

g(x) = 2x
g(x) = 2( x )
g(h(x)) = 2( h(x) ) ... replace every x with h(x)
g(h(x)) = 2( x^2-4 ) ... replace h(x) on the right side with x^2-4
g(h(x)) = 2x^2-8
(g o h)(x) = 2x^2-8

Now plug in x = 0
(g o h)(x) = 2x^2-8
(g o h)(0) = 2(0)^2-8
(g o h)(0) = 2(0)-8
(g o h)(0) = 0-8
(g o h)(0) = -8

Regardless of which method you use, the answer is -8

5 0
3 years ago
Math challenging and now math challenging me to challenge math
erastovalidia [21]

Answer:

$30

Step-by-step explanation:

Total amount paid by the hire purchase scheme:

$60 + 6 * $45 = $60 + $270 = $330

Total amount paid in just the cash price:

$300

Difference:

$330 - $300 = $30

3 0
3 years ago
How do you solve this problem? What is a rewritten form of the radical(-8/726) It is supposed to be a squar root sign instead of
Mamont248 [21]
I think the answer is negative 8 square root 726

then the answer if I am right sorry if I am not would be negative 88 square root 6

again sorry if wrong
5 0
3 years ago
Are these a function?​
Molodets [167]

Answer:

yes........these all are....

8 0
3 years ago
Read 2 more answers
Other questions:
  • What is the distance between the points (-7, -8) and (10, -8)
    14·1 answer
  • Plz help me find the unit rate and explain.
    13·1 answer
  • A multiple choice test has 9 questions each of which has 5 possible answers
    6·1 answer
  • What is the value of f(1)?
    15·1 answer
  • Find the indicated limit. ModifyingBelow lim With x right arrow 8 StartRoot 7 x minus 2 EndRoot Select the correct choice below
    15·1 answer
  • Which of the following functions are continuous for all real numbers? \begin{aligned} &h(x)= \log(x) \\\\ &g(x)=\cot(x)
    10·1 answer
  • Evan and Dana Each work two part-time jobs to earn $500 per week in order to pay bills. Evans college schedule allows him to wo
    8·1 answer
  • Percent of change
    13·1 answer
  • Please answer this question
    12·1 answer
  • Making late payments on credit card bills has what kind of effect on a person's credit score?
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!