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]
2 years ago
9

{ lnx } " align="absmiddle" class="latex-formula">
how do I differentiate this
Mathematics
1 answer:
Kamila [148]2 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
I need help with Algebra. is this a good site?​
forsale [732]

Answer:

Yes! I use this site all the time and my questions always get answered quickly!

Step-by-step explanation:

7 0
2 years ago
What is the y-intercept, axis of symmetry and vertex of the following function.
Pepsi [2]

Complete the square:

F(x) = -3x² - 6x - 5

F(x) = -3 (x² + 2x) - 5

F(x) = -3 (x² + 2x + 1 - 1) - 5

F(x) = -3 ((x + 1)² - 1) - 5

F(x) = -3 (x + 1)² + 3 - 5

F(x) = -3 (x + 1)² - 2

The y-intercept has x-coordinate equal to 0, so it corresponds to the value of F(0) :

F(0) = -3 (0 + 1)² - 2 = -3 - 2 = -5

The axis of symmetry is the vertical line running through the vertex of this parabola, so we'll come back to this.

The vertex of the parabola is (-1, -2). This represents the maximum value of F(x), which follows from

(x + 1)² ≥ 0   ⇒   -3 (x + 1)² ≤ 0   ⇒   -3 (x + 1)² - 2 ≤ -2

This is to say, every point on the parabola has a y-coordinate no greater than -2.

As mentioned earlier, the axis of symmetry is the vertical line through the vertex, and its equation is determined by the x-coordinate of the vertex. Hence the AoS is the line x = -1.

4 0
2 years ago
Read 2 more answers
What is 1+1<br> Who ever awnser first get brainlyist
Bas_tet [7]

Answer:

2

Step-by-step explanation:

Hope this helps, been doing it all my life! :P

8 0
3 years ago
Read 2 more answers
When writing numbers in base 10, we only allow coefficients of 0 through 9. Why is that?​
Margaret [11]

Answer:

Because 0 counts as the first possible number. 0-9 gives you 10 possible numbers.

Step-by-step explanation:

7 0
2 years ago
What is the distance between 3,0 and 6,-13
madam [21]

Answer:

√178

Step-by-step explanation:

Distance formula: d = \sqrt{(x2-x1)^2 + (y2-y1)^2}

Simply plug in your coordinates into the distance formula to find the distance between them.

8 0
2 years ago
Other questions:
  • Which expression is equivalent to 5!<br> 5^4*3^2<br> 5-4-3-2-1<br> 5.4.3-2.1<br> 5+4+3+2+1<br> 5.1
    5·1 answer
  • Evaluate 9 over m+4 when m=3
    9·1 answer
  • A grain of sand has a diameter of 0.049 millimeters. Write 0.049 in words.
    5·2 answers
  • Which of the following scenarios represents a combination? The number of ways 30 people can finish in the first 3 positions. The
    12·2 answers
  • Luke’s Bakery recently spent a total of $69 on new equipment, and their average hourly operating costs are $15. Their average ho
    7·1 answer
  • What the slope (0,-1) and (2,-5)​
    5·2 answers
  • What is 450 increased by 75%
    10·1 answer
  • I don’t understand graphing.
    5·1 answer
  • The length of a rectangle is 6 m longer than its width.
    14·1 answer
  • Josiah downloads 44 songs, including 16 songs by his favorite band.
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!