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3 years ago

Derivatives of inverse trigonometric functions please explain answers

Mathematics

1 answer:

Jobisdone [24]3 years ago

6 0

I'll explain how to do the first one:-

y = cos-1(x2)

This can be described as ' a function of a function' x^2 is a function of x and cos-1(x^2) is a function of x^2.

We need to apply the chain rule.

Personally I find this easier to understand if i let u = x^2, so

If y = f(u) and u is a function of x then

dy/dx = dy/ du * du/dx

Here u = x^2 and y = cos-1(u)

du/dx = 2x

so dy/dx = d(cos-1(x^2) dx = dy/du * du/dx

= -1 / √(1 - u^2) * 2x

= -2x / √(1 - u^2)

= -2x / √(1 - (x^2)^2)

= -2x / √(1 - x^4)

I hope this helps. but if not. you might like to employ the formulae in the question - The square boxes contain the 'u' s in my answer. These formulae are equivalent to my explanation.

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What is the number that has the same absolute value as 81

LenaWriter [7]

The absolute value of -81 has the same absolute value as that of 81 because they both have the same distance to 0.

4 0

3 years ago

Samantha is making flower arrangements. She has 32 roses and 96 daisies. If she wants to make all the arrangements identical and

-Dominant- [34]

Answer:

3 daisies.

Step-by-step explanation:

Given that,

Samantha has 32 roses and 96 daisies.

She wants to make all the arrangements identical and have no flowers left over. We need to find the no of daisies in each flower arrangement.

For this, we need to first find the HCF of 32 and 96.

The factors of 32 are: 1, 2, 4, 8, 16, 32

The factors of 96 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96

HCF = 32

No of daisies = 96/32 = 3

Hence, there are 3 daisies in each flower arrangement.

7 0

3 years ago

Which system of inequalities does the graph represent? Which test point satisfies both of the inequalities in that system?

AveGali [126]

Answer:

1) The inequality for the given system are

y ≥ 4x - 4

y ≥ x - 1.5

2) The test point (0,0) satisfies both of the inequalities in the system represented by the graph.

Step-by-step explanation:

Given : A graph showing a system of inequalities.

We have to find the system of inequality.

For line 1)

The points that cut the x and y axis are (1,0) and (0,-4)

Thus, we can find the equation of line using two given point.

Since the general equation of line is y = mx + c

Where m is slope and c is y intercept

Slope is find as $m=\frac{y_2-y_1}{x_2-x_1}$

Substitute, we get,

$m=\frac{-4-0}{0-1}=4$

Slope is 4.

Thus, equation becomes y = 4x + c

For c put (0,-4) in the above equation , we have,

-4 = 4(0) + c ⇒ c = -4

Thus, equation becomes y = 4x - 4

For inequality take a test point (0,0) and we check for which inequality it satisfies the graph region

For (0,0)

y = 4x - 4 becomes 0 = - 4 is satisfied when 0 > -4

thus, the inequality becomes y ≥ 4x - 4

Since, the line is a solid so it will take up equality sign too.

For line 2)

The points that cut the x and y axis are (1.5,0) and (0,-1.5)

Thus, we can find the equation of line using two given point.

Since the general equation of line is y = mx + c

Where m is slope and c is y intercept

Slope is find as $m=\frac{y_2-y_1}{x_2-x_1}$

Substitute, we get,

$m=\frac{-1.5-0}{0-1.5}=1$

Slope is 1.

Thus, equation becomes y = x + c

For c put (0,-1.5) in the above equation , we have,

-1.5 = (0) + c ⇒ c = - 1.5

Thus, equation becomes y = x - 1.5

For inequality take a test point (0,0) and we check for which inequality it satisfies the graph region

For (0,0)

y = x - 1.5 becomes 0 = -1.5 is satisfied when 0 > - 1.5

thus, the inequality becomes y ≥ x - 1.5

Since, the line is a solid so it will take up equality sign too.

Thus, the inequality for the given system are

y ≥ 4x - 4

y ≥ x - 1.5

Also, The test point (0,0) satisfies both of the inequalities in the system represented by the graph.

6 0

3 years ago

Can somebody help me What is 4(x-1)=6

avanturin [10]

4(x-1)=6 you start by dividing the whole equation by 4, so
x-1=6/4 simplify, x-1=3/2 then you add 1 to the whole equation
x=1 and 3/2 or x=5/2

7 0

3 years ago

Use<br> with numbers. Use<br> with shapes.

riadik2000 [5.3K]

Answer:

Can you clarify?

Step-by-step explanation:

5 0

3 years ago