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3 years ago

Can someone help please?????

Mathematics

1 answer:

frutty [35]3 years ago

8 0

The answer is 13 you have to add the top and bottom

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How to differentiate ?

Bas_tet [7]

Use the power, product, and chain rules:

$y = x^2 (3x-1)^3$

• product rule

$\dfrac{\mathrm dy}{\mathrm dx} = \dfrac{\mathrm d(x^2)}{\mathrm dx}\times(3x-1)^3 + x^2\times\dfrac{\mathrm d(3x-1)^3}{\mathrm dx}$

• power rule for the first term, and power/chain rules for the second term:

$\dfrac{\mathrm dy}{\mathrm dx} = 2x\times(3x-1)^3 + x^2\times3(x-1)^2\times\dfrac{\mathrm d(3x-1)}{\mathrm dx}$

• power rule

$\dfrac{\mathrm dy}{\mathrm dx} = 2x\times(3x-1)^3 + x^2\times3(3x-1)^2\times3$

Now simplify.

$\dfrac{\mathrm dy}{\mathrm dx} = 2x(3x-1)^3 + 9x^2(3x-1)^2 \\\\ \dfrac{\mathrm dy}{\mathrm dx} = x(3x-1)^2 \times (2(3x-1) + 9x) \\\\ \boxed{\dfrac{\mathrm dy}{\mathrm dx} = x(3x-1)^2(15x-2)}$

You could also use logarithmic differentiation, which involves taking logarithms of both sides and differentiating with the chain rule.

On the right side, the logarithm of a product can be expanded as a sum of logarithms. Then use other properties of logarithms to simplify

$\ln(y) = \ln\left(x^2(3x-1)^3\right) \\\\ \ln(y) = \ln\left(x^2\right) + \ln\left((3x-1)^3\right) \\\\ \ln(y) = 2\ln(x) + 3\ln(3x-1)$

Differentiate both sides and you end up with the same derivative:

$\dfrac1y\dfrac{\mathrm dy}{\mathrm dx} = \dfrac2x + \dfrac9{3x-1} \\\\ \dfrac1y\dfrac{\mathrm dy}{\mathrm dx} = \dfrac{15x-2}{x(3x-1)} \\\\ \dfrac{\mathrm dy}{\mathrm dx} = \dfrac{15x-2}{x(3x-1)} \times x^2(3x-1)^3 \\\\ \dfrac{\mathrm dy}{\mathrm dx} = x(15x-2)(3x-1)^2$

7 0

2 years ago

Eight students share 12 mini oatmeal muffins equally and 6 students share 15 mini apple muffins equally. Carmine is in both grou

Lynna [10]

12 for 8 that is 1.5 per person
15 for 6 that is 2.5 per person

She would get 4 muffins

Hope this helps

8 0

3 years ago

According to the key of a particular park map, every 8 inches on the map represents 3 miles of trails in the park. How many inch

MA_775_DIABLO [31]

Answer:

24 inches represents 9 miles in the map

Step-by-step explanation:

To solve this problem you take into account that 8 inches represents 3 miles and that x represent the number of inches for 9 miles. That is:

8 ------- 3

x ------- 9

This is simply a rule of three, then you calculate:

$x=\frac{8\ x\ 9}{3}=\frac{72}{3}=24$

Hence, 24 inches represents 9 miles in the map

8 0

3 years ago

What is the solution to this system of equations y=x-2 y=-0.5x+4

gladu [14]

Answer:

Substitute y=x-2y=x−2 into y=-0.5x+4y=−0.5x+4.

x-2=-0.5x+4x−2=−0.5x+4

2 Solve for xx in x-2=-0.5x+4x−2=−0.5x+4.

x=4x=4

3 Substitute x=4x=4 into y=x-2y=x−2.

y=2y=2

4 Therefore,

\begin{aligned}&x=4\\&y=2\end{aligned}

x=4

y=2

Step-by-step explanation:

6 0

2 years ago

In a movie theater, there are children and adults in the ratio 4:7. If there are 21 adults, how many people total are there in t

lozanna [386]

Answer:

Step-by-step explanation:

7x3=21

4x3=12

21+12=33

8 0

3 years ago