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3 years ago

Please help me with this math problem.

Mathematics

1 answer:

devlian [24]3 years ago

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Use logarithmic differentiation to find the derivative of the function. y = x2cos x Part 1 of 4 Using properties of logarithms,

Arisa [49]

ANSWER

${y}^{'} = 2x \cos(x) - {x}^{2} \sin(x)$

EXPLANATION

The given function is

$y = {x}^{2} \cos(x)$

We take natural log of both sides;

$ln(y) = ln({x}^{2} \cos(x) )$

Recall and use the product rule of logarithms.

$ln(AB) = ln(A ) + ln(B)$

This implies that:

$ln(y) = ln({x}^{2} ) + ln( \cos(x) )$

$ln(y) = 2 ln({x} ) + ln( \cos(x) )$

We now differentiate implicitly to obtain;

$\frac{ {y}^{'} }{y} = \frac{2}{x} - \frac{ \sin(x) }{ \cos(x) }$

Multiply through by y,

${y}^{'} = y( \frac{2}{x} - \frac{ \sin(x) }{ \cos(x) ) })$

Substitute y=x²cosx to obtain;

${y}^{'} = {x}^{2} \cos(x) ( \frac{2}{x} - \frac{ \sin(x) }{ \cos(x) ) } )$

Expand:

${y}^{'} = 2x \cos(x) - {x}^{2} \sin(x)$

7 0

3 years ago

In a city, 6th and 7th Avenues are parallel and the corner that The Pizza Palace is on is a 54° angle. What is the

goblinko [34]

The answer is C because it is telling you to subtract 180 degrees from 54 degrees to get the final answer which is 126 I got that because 54 is that angle and it is asking for the whole amount so it would be C

7 0

3 years ago

Read 2 more answers

Identify the maximum of the graph below. Type your answer by filling in the blanks below

nevsk [136]

Answer:

The maximum point of this function is (5,4).

Step-by-step explanation:

The maximum of a function is the maximum value that it can take.

Seeing the graph we can say that the maximum value of y occurs at x = 4. Here y = 5 corresponds to this value of x.

Therefore, the maximum point of this function is (5,4).

I hope it helps you!

8 0

3 years ago

HELP NEEDED , YOU WILL GET 10 POINTS !

Nitella [24]

Answer:

stop cheating on your schoology test;)

Step-by-step explanation:

8 0

3 years ago

Find the ordered pair (x,y) that is a solution to the equation.

miv72 [106K]

Answer:

☑ (¼, 0)

Step-by-step explanation:

${ \tt{4x - y = 1}}$

» Assume y is zero:

${ \tt{4x - 0 = 1}} \\ { \tt{4x = 1}} \\ { \tt{x = \frac{1}{4} }}$

4 0

3 years ago