The function given is a composite function. Let's work from the outside in:
First step:
![\frac{d}{dx}[y]= \frac{d}{dx}[ln(sinh(2x))]](https://tex.z-dn.net/?f=%20%5Cfrac%7Bd%7D%7Bdx%7D%5By%5D%3D%20%5Cfrac%7Bd%7D%7Bdx%7D%5Bln%28sinh%282x%29%29%5D)
Now, let's work it out:
![\frac{dy}{dx} = \frac{1}{sinh(2x) } * \frac{d}{dx}[sinh(2x)]](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%20%5Cfrac%7B1%7D%7Bsinh%282x%29%20%7D%20%2A%20%20%20%5Cfrac%7Bd%7D%7Bdx%7D%5Bsinh%282x%29%5D)
Next step:
![\frac{dy}{dx} = \frac{1}{sinh(2x) } * cosh(2x) * \frac{d}{dx}[2x]](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%20%5Cfrac%7B1%7D%7Bsinh%282x%29%20%7D%20%2A%20cosh%282x%29%20%2A%20%20%5Cfrac%7Bd%7D%7Bdx%7D%5B2x%5D%20)
Next step:
Simplify:
Simplify further:
Remember that:
So,
your final answer is:
So, your answer is
C. Hope I could help you!
Answer:
y intercept is (0, 1)
slope is 3
equation is y = 3x +1
Step-by-step explanation:
You find the y intercept when x equals 0 and you can see that on the table that is 1.
You find slope by y2-y1 divided by x2-x1. if you pick (0,1) and (1,4) it is 4-1/1-0 which equals 3.
Therefore the equation is y = 3x + 1 in slope intercept form because the slope is 3 and y int is 1.
Assuming you mean flutes 5: clarinets 4: trumpets 3...
Question 1 Answer: There are <u>36 trumpets</u>
Question 1 Explanation: 60/5=12 (the amount it went up in ratio), then multiply 12 by each of the other ratios. If there are 60 flutes then there are 48 clarinets (4*12) and 36 trumpets (3*12). If you want to check work, you can then divide answer back by 12 and get the ratio again.
Assuming there are no other type of band instruments in Carver's band then...
Question 2 Answer:There are 50 flutes, <u>40 </u>clarinets, and 30 trumpets.
Question 2 Explanation: add the ratio then divide it by the number of band people (5+4+3=12: 120/12=10) this answer is then what you multiply for each ratio. So, flutes 5*10=50, clarinets 4*10=40, trumpets 3*10=30. 50+40+30=120. Therefore, if there are no other type of band instruments in Carver's band there are 40 people who play the clarinet (unless of course some are played by computers/robots or an amazing person can play multiple at a time.
[9(10-2)]=[2+(5 x 2)]
90-18= 2 + 10
72= 12
72 divided by 12
Answer = 6
