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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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3. At the start of summer, Ben has $250 . He takes a summer
earnstyle [38]

Answer:

Week 4

Step-by-step explanation:

Ben has $250 in the beginning.  He saves $150 per week.

y = 150x + 250

Tim has $1,650 in the beginning.  He spends $200 per week.

y = 1650 - 200x

We are trying to find which x-value produces the same y-value for both equations.  You can do this by setting both equations equal to each other.

150x + 250 = 1650 - 200x

(150x + 250) + 200x = (1650 - 200x) + 200x

350x + 250 = 1650

(350x + 250) - 250 = (1650) - 250

350x = 1400

(350x)/350 = (1400)/350

x = 4

By week 4, they will have the same amount of money.

3 0
3 years ago
Solve the equation using the distributive property and properties ofequally 1/2 (x+6)=18 what is the value of X
Natali [406]

x = 30

The distributive property says that we need to multiply what's in the brackets by 1/2 (so 1/2*x and 1/2*6) to get the equation 1/2x + 3 = 18.

Then we need to subtract our constant, 3, from boths sides to get 1/2x = 15.

Multiply both sides by two to isolate x and you get x = 30.

Hope this helps! :)

7 0
3 years ago
Pls help I will give brainliest
miss Akunina [59]

Answer:

Step-by-step explanation:

the distance around the figure--we need to find the perimeter

we have rectangle that has the side, 8 and 15

P(r)=2(8)+2(15)=16+30=46

we also have half of the circle with the diameter =8 and r=4

Circumference =2*3.14*r

C=2*3.14*4=25.12

we need just half of the circle 25.12/2=12.56

P figure=46+12.56=58.56

Area= rectangle=l*w=8*15=120

Area(circle)=3.14*r^2=3.14*16=50.24

half circle 50.24/2=25.12

Area figure=120+25.12=145.12

6 0
3 years ago
What's three fourths times twenty eight equal?
Hoochie [10]
Hi , 3/4 times 28 equals to 84/4
28 is equivalent to 28/1
we just multiply straight across
28 x 3 equals to 84
4 x 1 equals to 4
 
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5 0
3 years ago
Read 2 more answers
Help me pls divide and i will make u a BRAINLIEST
seropon [69]

Answer:

1.4

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
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