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
Lemur [1.5K]
3 years ago
9

{ lnx } " align="absmiddle" class="latex-formula">
how do I differentiate this
Mathematics
1 answer:
Kamila [148]3 years ago
3 0

Use the power rule for differentiation:

\dfrac{\text{d}}{\text{d}x} (f(x))^k = k(f(x))^{k-1}f'(x)

You can use this formula if you remember that a root is just a rational exponential:

\sqrt[4]\ln(x) = (\ln(x))^{\frac{1}{4}}

So, remembering that the derivative of the logarithm is 1/x, you have

\dfrac{\text{d}}{\text{d}x} (\ln(x))^{\frac{1}{4}} = \frac{1}{4}(\ln(x))^{\frac{1}{4}-1}\dfrac{1}{x}

Which you can rewrite as

\dfrac{1}{4}(\ln(x))^{\frac{1}{4}-1}\dfrac{1}{x} =\dfrac{1}{4}(\ln(x))^{\frac{-3}{4}}\dfrac{1}{x} =\dfrac{1}{4}\dfrac{1}{\sqrt[4]{\ln(x))^3}}\dfrac{1}{x} = \dfrac{1}{4x\sqrt[4]{\ln(x))^3}}

You might be interested in
Write an equation of the line that passes through the points (-3,-4) and (0,2)
nexus9112 [7]

Answer:

the answer is 2, hope this helps :)

8 0
2 years ago
11/7 in a mixed fraction
Mama L [17]
7 goes into 11 one time, which leaves you with 1 4/7.
6 0
3 years ago
Read 2 more answers
Para embalar una caja se emplea 4,2 m de cinta adhesiva. ?Cuántas cajas se podrán embalar con tres rollos que tienen 3 hm, 7 dam
kompoz [17]

For this case, we perform the conversions:

First roll:

1 \ Hectometer --------> 100 \ meters\\3 \ Hectometer --------> x

x = \frac {3 * 100} {1}\\x = 300 \ meters.

We make a rule of three to determine the number of "c" boxes that can be packed with 300 meters of adhesive tape.

1 -----------> 4.2

c -----------> 300

c = \frac {300 * 1} {4.2}\\c = 71.42857143\\c = 71

You can pack 71 boxes.

Second roll:

1 \ Decametro --------> 10 \ meters\\7 \ Decameter --------> x\\x = \frac {7 * 10} {1}\\x = 70 \ meters.

We make a rule of three to determine the number of "c" boxes that can be packed with 70 meters of adhesive tape.

1 -----------> 4.2

c -----------> 70

c = \frac {70 * 1} {4.2}\\c = 16.66666667\\c = 16

You can pack 16 boxes.

Third roll:

1 -----------> 4.2

c -----------> 50

c = \frac {50 * 1} {4.2}\\c = 11.9047619\\c = 11

You can pack 11 boxes.

Thus, in total you can pack11 + 16 + 71 = 98 \ boxes

Answer:

98 boxes

4 0
3 years ago
Use the rules for multiplication by powers of 10 to calculate 3 × 100
padilas [110]
3 × 100 = 300

the easiest way to do it is just add the same amount of zero's to the number you multiplied with. for example

3 × 10000 if you would just take out the zero's
it would look like this. 3 × 1

the answer of course would be 3 then you can put the zero's back in the answer (30000)

at least that's how I understood it

3 × 100 =

3 × 1(00) =
-->

-->
(00)
3 × 1(00) = 3

3 × 100 = 300
4 0
3 years ago
What is the simplified form of square root of 144x^36?
trasher [3.6K]

Answer:

The correct option is B.

Step-by-step explanation:

The given expression is

\sqrt{144x^{36}}

Use the property of radicals.

\sqrt{ab}=\sqrt{a}\sqrt{b}

\sqrt{144x^{36}}=\sqrt{144}\times \sqrt{x^{36}}

Use the property of exponent.

a^{mn}=(a^m)^n

\sqrt{144x^{36}}=12\times \sqrt{(x^{18})^2}

\sqrt{144x^{36}}=12\times x^{18}

\sqrt{144x^{36}}=12x^{18}

Therefore option B is correct.

3 0
3 years ago
Read 2 more answers
Other questions:
  • Kenyan bought 3.4 pounds of nails for his construction job. Each pound cost $1.59. How much did he pay for the nails? Round to t
    8·1 answer
  • Write the numeral for fifty million and sixty thousand​
    14·2 answers
  • A cube has a side length of 7 in. What is the volume of the cube? in3
    13·2 answers
  • Can someone tell me how to do this ?
    15·1 answer
  • Aaron is 1 year younger than Laura. The sum of their ages is 23 years. How old is each of them
    12·2 answers
  • Como se daca el area de un triangulo​
    12·1 answer
  • A one-tailed test is a a. hypothesis test in which rejection region is in one tail of the sampling distribution b. hypothesis te
    9·1 answer
  • 1 free pass to heaven if you help and get it right
    8·2 answers
  • (0.2÷–0.5+0.1)÷6?????????????????
    13·2 answers
  • What is the greatest number of tables that can be made? Explain how did you decide on this number?
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!