E. 5x+3 = 28
5x = 28 - 3
Divide by 5
Final answer = 5
F. 3x-9 = 18
3x = 18 + 9
18 + 9 = 27
Divide by 3
Final answer: 9
G. 8x-1=7
8x = 7 + 1
7 + 1 = 8
8x = 8
Divide by 8
Final answer: 1
H. 3x+5 = 10
3x = 10 - 5
10 - 5 = 5
Divide by 3
Final answer: 5/3
i. 13 + 7x = -1
7x = -1 - 13
-1 - 13 = -14
Divide by 7
Final answer: -2
j. 14 = 3x + 5
-3x + 14 = 5
-3x = 5 - 14
-3x = -9
Divide by - 3
Final answer: 3
K. 4x - 7 = -13
4x = -13 + 7
4x = -6
Divide by 4
Final answer: -3/2
l. -3 = 2x+ 9
-2x - 3 = 9
-2x = 9 + 3
9 + 3 = 12
2x = 12
Divide it by -2
Final answer: -6
To find the derivative of this function, there is a property that we should know called the Constant Multiple Rule, which says:
![\dfrac{d}{dx}[cf(x)] = cf'(x)](https://tex.z-dn.net/?f=%5Cdfrac%7Bd%7D%7Bdx%7D%5Bcf%28x%29%5D%20%3D%20cf%27%28x%29)
(where 
is a constant)
Remember that the derivative of 
is 
. However, you may notice that we are finding the derivative of 
, not 
. So, we are going to have to use the chain rule. To complete the chain rule for the derivative of a trigonometric function (in layman's terms) is basically the following: First, complete the derivative of the trig function as you would if what was inside the trig function is 
. Then, take the derivative of what's inside of the trig function and multiply it by what you found in the first step.
Let's apply that to our problem. Right now, I am not going to worry about the 
at the front of the equation, since we can just multiply it back in at the end of our problem. So, let's examine 
. We see that what's inside the trig function is 
, which has a derivative of 2. Thus, let's first find the derivative of as if was just and then multiply it by 2.
The derivative of would first be 
. Multiplying it by 2, we get our derivative of 
. However, don't forget to multiply it by the that we removed near the beginning. This gives us our final derivative of .
Remember that we now have to find the derivative at the given point. To do this, simply "plug in" the point into the derivative using the x-coordinate. This is shown below:
![-\cot[2(\dfrac{\pi}{4})]\csc[2(\dfrac{\pi}{4})]](https://tex.z-dn.net/?f=-%5Ccot%5B2%28%5Cdfrac%7B%5Cpi%7D%7B4%7D%29%5D%5Ccsc%5B2%28%5Cdfrac%7B%5Cpi%7D%7B4%7D%29%5D)
Our final answer is 0.
Steps:
1. 6x=4y + 7
2. You have to write it in slope intercept to get the slope and y-intercept.
3. Subtract 7 on both sides
4y= 6x-7
4. Divide everything by 4
5. Y= 3/2x + -7/4
6. Slope= 3/2 y-intercept= -7/4
