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
Ludmilka [50]
2 years ago
11

Someone please help !! I don’t know what I’m doing with this !!

Mathematics
1 answer:
dimulka [17.4K]2 years ago
7 0

Answer:

  a) d(sinh(f(x)))/dx = cosh(f(x))·df(x)/dx

  b) d(cosh(f(x))/dx = sinh(f(x))·df(x)/dx

  c) d(tanh(f(x))/dx = sech(f(x))²·df(x)/dx

  d) d(sech(4x+2))/dx = -4sech(4x+2)tanh(4x+2)

Step-by-step explanation:

To do these, you need to be familiar with the derivatives of hyperbolic functions and with the chain rule.

The chain rule tells you that ...

  (f(g(x)))' = f'(g(x))g'(x) . . . . where the prime indicates the derivative

The attached table tells you the derivatives of the hyperbolic trig functions, so you can answer the first three easily.

__

a) sinh(u)' = sinh'(u)·u' = cosh(u)·u'

For u = f(x), this becomes ...

  sinh(f(x))' = cosh(f(x))·f'(x)

__

b) After the same pattern as in (a), ...

  cosh(f(x))' = sinh(f(x))·f'(x)

__

c) Similarly, ...

  tanh(f(x))' = sech(f(x))²·f'(x)

__

d) For this one, we need the derivative of sech(x) = 1/cosh(x). The power rule applies, so we have ...

  sech(x)' = (cosh(x)^-1)' = -1/cosh(x)²·cosh'(x) = -sinh(x)/cosh(x)²

  sech(x)' = -sech(x)·tanh(x) . . . . . basic formula

Now, we will use this as above.

  sech(4x+2)' = -sech(4x+2)·tanh(4x+2)·(4x+2)'

  sech(4x+2)' = -4·sech(4x+2)·tanh(4x+2)

_____

Here we have used the "prime" notation rather than d( )/dx to indicate the derivative with respect to x. You need to use the notation expected by your grader.

__

<em>Additional comment on notation</em>

Some places we have used fun(x)' and others we have used fun'(x). These are essentially interchangeable when the argument is x. When the argument is some function of x, we mean fun(u)' to be the derivative of the function after it has been evaluated with u as an argument. We mean fun'(u) to be the derivative of the function, which is then evaluated with u as an argument. This distinction makes it possible to write the chain rule as ...

  f(u)' = f'(u)u'

without getting involved in infinite recursion.

You might be interested in
5 Points |<br> Which of the following are remote interior angles of 6? Check all that apply.
aniked [119]

Answer: 1 and 3

Step-by-step explanation:

I had the same question on my test the other day hope this helped.

4 0
3 years ago
1. What are the intercepts of the equation 2x+3/2y+3z=6
Roman55 [17]
Use
Math
Way
It can tell u
Or
Photo
Math
4 0
3 years ago
Read 2 more answers
Help quickly please!!!
vagabundo [1.1K]

Answer:

1/3 B h

1/3(50.24)(10)

plug in into a calculator

6 0
3 years ago
10x4thousands=______thousands=
Zepler [3.9K]
The answer is 40 thousands
7 0
3 years ago
Find the distance between the points (4,5) and (10, – 3). Round decimals to the nearest tenth
Ilia_Sergeevich [38]

Answer:

10 is the distance.

3 0
3 years ago
Other questions:
  • Three cards are drawn sequentially from a shuffled deck without replacement. What is the approximate probability all three drawn
    5·1 answer
  • Eight more than twice a number is eight. Find the number.
    7·2 answers
  • The area of a rectangle is represented with the expression (18x-12) inches squared. The width of the rectangle is 6 inches. Writ
    15·1 answer
  • Select all of the following that are ordered pairs of the given function.
    7·2 answers
  • This using the substitution method
    8·1 answer
  • $210 watch; 20% discount
    9·2 answers
  • Total of y and five divided by x
    7·2 answers
  • Please help! I neeeeeeeeeeeeddddddddd HELP!
    15·2 answers
  • Solve for x.
    10·1 answer
  • Could someone help me with number 19. PLEASE! thanks. :)
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!