1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Lerok [7]
3 years ago
7

Need help with Calculus 1 inverse trig functions

Mathematics
1 answer:
lidiya [134]3 years ago
8 0

Answer:

\displaystyle y'=3\frac{1+\frac{x}{\sqrt{1+x^2}}}{2+2x^2+2x\sqrt{1+x^2}}

Step-by-step explanation:

<u>The Derivative of a Function</u>

The derivative of f, also known as the instantaneous rate of change, or the slope of the tangent line to the graph of f, can be computed by the definition formula

\displaystyle f'(x)=\lim\limits_{\Delta x \rightarrow 0}\frac{f(x+\Delta x)-f(x)}{\Delta x}

There are tables where the derivative of all known functions are provided for an easy calculation of specific functions.

The derivative of the inverse tangent is given as

\displaystyle (tan^{-1}u)'=\frac{u'}{1+u^2}

Where u is a function of x as provided:

y=3tan^{-1}(x+\sqrt{1+x^2})

If we set

u=(x+\sqrt{1+x^2})

Then

\displaystyle u'=1+\frac{2x}{2\sqrt{1+x^2}}

\displaystyle u'=1+\frac{x}{\sqrt{1+x^2}}

Taking the derivative of y

y'=3[tan^{-1}(x+\sqrt{1+x^2})]'

Using the change of variables

\displaystyle y'=3[tan^{-1}u]'=3\frac{u'}{1+u^2}

\displaystyle y'=3\frac{u'}{1+u^2}=3\frac{1+\frac{x}{\sqrt{1+x^2}}}{1+(x+\sqrt{1+x^2})^2}

Operating

\displaystyle y'=3\frac{1+\frac{x}{\sqrt{1+x^2}}}{1+x^2+2x\sqrt{1+x^2}+1+x^2}

\boxed{\displaystyle y'=3\frac{1+\frac{x}{\sqrt{1+x^2}}}{2+2x^2+2x\sqrt{1+x^2}}}

You might be interested in
I need a answer to 77.5% of 13.270​
den301095 [7]

Answer:

10.28425

Step-by-step explanation:

4 0
3 years ago
As part of a study done for a large corporation, psychologists asked randomly selected employees to solve a collection of simple
zhenek [66]

Answer:

P(A')=1-0.411=0.589

And that represent the probability that they take longer than 7 minutes to solve the puzzles.

Step-by-step explanation:

The complement rule is a theorem that provides a connection between the probability of an event and the probability of the complement of the event. Lat A the event of interest and A' the complement. The rule is defined by: P(A)+P(A') =1

On this case we have that n= 56 represent the employees selected to solve the puzzles.

We know that 23 out of the 56 selected solved the puzzles in less than 7 minutes.

Let's define the events A and A' like this:

A: Employees solved puzzles in less than 7 minutes

By the complement rule then:

A' : Employees solved puzzles in more than 7 minutes

Based on this we are interested to find the probability for A'

We can begin finding P(A), from the definition of probability we know:

P(A)=\frac{Possible outcomes}{Total outcomes}

For this case if we replace we got:

P(A) =\frac{23}{56}=0.411

And using the complemnt rule we got:

0.411 +P(A')=1

And solving for P(A') we got:

P(A')=1-0.411=0.589

And that represent the probability that they take longer than 7 minutes to solve the puzzles.

4 0
2 years ago
(08.01, 08.02, 08.03, 08.05, 08.06 MC)
fenix001 [56]
Is it x times 2 times y times 2? is that what it is asking or is it meaning squared
6 0
3 years ago
Read 2 more answers
Identify how the Virginia declaration of rights helped lead to an expansion of civil rights both in the state of Virginia and la
-BARSIC- [3]

Answer:

yeah

Step-by-step explanation:

wrong subject dude

things go wrong sometimes

you lost 46 points

\lim_{n \to \infty} a_n

7 0
3 years ago
Write the equation of a line perpendicular to y=-5x that passes through the point (1,1) in slope intercept form. (This question
Kazeer [188]

Answer:

y= 1/5x + 0.8

Step-by-step explanation:

Hope this helps

7 0
2 years ago
Other questions:
  • If 4 - 7x = 39 then what is the value of x + 1
    14·1 answer
  • Use the Remainder Theorem to find the remainder for (4x^3+4x^2+2x+3)/(x-1) and state whether or not the binomial is a factor of
    15·2 answers
  • Look at the triangle:
    9·1 answer
  • What is the measure of
    10·2 answers
  • Is 4(y-30)=4y+12 how many solutions
    10·1 answer
  • The area of a rectangle is 20 square meters. How long is the length, if the width is 4 meters?
    8·1 answer
  • Please help - will mark brainlest
    11·1 answer
  • Calculate the volume.<br> Plz hurry!! 40 points in it!!
    13·1 answer
  • Calculate the slope of the line that passes through the points (1, −3) and (3, −5).
    13·1 answer
  • Best Answer gets BRAINLIEST!!!
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!