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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}}

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There is a circle with a center of 0,0 on a coordinate plane. There is one point on the circle's circumference in which the x:y
abruzzese [7]

Answer:

Step-by-step explanation:

Suppose the radius is 1. The parametric equations for the circle are

x = cosθ

y = sinθ

x:y = 3:1

tanθ = ⅓

cosθ = 3/√(1²+3²) =  3/√10

sinθ = 1/√10

The solutions are (3/√10, 1/√10) and (-3/√10, -1/√10).

6 0
3 years ago
The difference of a number and 6 is -11. What is the number?
Citrus2011 [14]

Answer:

The number is 17

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
|y-9|=6<br><br><br>a. y=-15, y=-3<br><br>b. y=-15, y=15<br><br>c. y=3, y=15<br><br>d.y=-3, y=3
ELEN [110]
I hope you get it.
Be safe!

4 0
3 years ago
Help please, I’m confused and could you please explain the best you can do I understand? Thank you so much if you decide to help
ElenaW [278]

A ray is basically a line that has a "fixed point" on one end (this would be represented by a shaded circle on one end) and the opposite end goes to infinity (this would be represented by an arrow). The first image below is an example of a ray.

When writing rays out you must write it like in the third image below. Note that there is a "ray" on top of the "letters". The letter that signifies the end point (In the example below this would be "A") is under the side that has NO arrow symbol, and the letter that signifies the continues end is under the side of the ray that HAS the arrow. In other words the "formula" for writing out rays is:

End point; infinite end

We must find four rays with the endpoint E. This means that the "fixed point" must be E and the other end must continue indefinitely.

In the second image below I have colored each ray with the end point E in a different color.

First we have the ray EA (I don't know how to make the ray symbol on here so just assume that above EA the arrow looks like so: --->)

Next is ray EG (again the symbol above EG is --->)

Next is the ray ED (symbol above ED is --->)

Finally EF is a ray with the end point E (symbol above EF is --->)

When looking at the answer choices the only two that even use the correct symbol is B and C.

The issue with option C is that the end point (E) doesn't come first when they wrote it out.

That makes the answer B!

Hope this helped!

~Just a girl in love with Shawn Mendes

~Just a girl in love with Shawn Mendes

4 0
3 years ago
Read 2 more answers
What is the answer to his question
horsena [70]

Answer:

A. 720 per hour

Step-by-step explanation:

1200+ <em>720</em> + 720 + <u>360</u> =3000

        <em>hr 1↑</em>+ hr 2↑ + <u>↑30 min</u>

8 0
3 years ago
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