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Ne4ueva [31]
3 years ago
11

In order to solve this equation for x, the first step is to subtract 6 from both sides.

Mathematics
2 answers:
Tcecarenko [31]3 years ago
7 0
True. You would end up with 3x=36
telo118 [61]3 years ago
3 0
The statement is true.
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Someone please help !! I don’t know what I’m doing with this !!
dimulka [17.4K]

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.

7 0
3 years ago
What is the value of 5/zwhen z=2
AveGali [126]

Step-by-step explanation:

When

z = 2

Then

5/z

= 5 / 2

= 2.5

Hope it will help :)

7 0
3 years ago
Can someone explain and answer this for me??
OleMash [197]
The mistake is in line 2, the parenthesis means multiplication therefore it has to be 3x
4 0
3 years ago
Can someone pls help me with this
Over [174]
i believe it is 2 i took the test but it was a while ago sorry if it’s wrong!
4 0
3 years ago
On a coordinate plane the vertices of a triangle are A(-1, 4), B(-3,2), and C(0, -1). Find the coordinates of the
Llana [10]

Answer:

B) (-2,3)

Step-by-step explanation:

Graph all your points. No count the distance from point A to B. divide in half .

5 0
3 years ago
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