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3 years ago

Can someone help me with this?

Mathematics

1 answer:

Anna007 [38]3 years ago

3 0

$\frac{7}{8} - \frac{1}{2}$
$= \frac{7}{8} - \frac{4}{8}$
$= \frac{3}{8}$

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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

Solve the system of equations by substitution<br> 5x +y = 36<br> y = 4x

natali 33 [55]

Step-by-step explanation:

The answer is mentioned above.

7 0

3 years ago

Read 2 more answers

Write the equation in y=mx+b form please????

Solnce55 [7]

ANSWER

$y = - 2x - 5$

EXPLANATION

We can use any two points to determine the slope.

The line passes through;

(-3,1) and (-5,5).

The slope is given by

$m = \frac{y_2-y_1}{x_2-x_1}$

This implies that;

$m = \frac{5 - 1}{ - 5 - - 3}$

$m = \frac{4}{ - 2} = - 2$

We can now find the equation using the formula;

$y-y_1=m(x-x_1)$

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

Expand:

$y = - 2x -6 + 1$

$y = - 2x - 5$

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3 years ago

Geela makes orange paint with 5 parts yellow to

Oxana [17]

Answer:

Geela would need 9 yellow parts

Explanation:

Originally, the Geela needed more yellow than red and the difference was 4 parts.

6-2=4 parts

4 parts + 5 parts of yellow = 9 yellow parts.

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2 years ago

Determine the interquartile range for the data.<br> 16, 19, 25, 20,<br> 22, 21, 17, 20

Roman55 [17]

Answer:

the answer is 15 subtract the highest number from the lowest

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3 years ago