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.
Answer:
Step-by-step explanation:
Let number of large bags be x
Let number of large bags be x
Teddy will buy at least 15 bags of ice for the graduation picnic.
Each large bag of ice costs $4.00, and each small bag of ice costs $2.50. He will spend up to $50 on ice. The set of inequalities that describe this scenario are
4x + 2.5y lesser than or equal 50
x + y greater than 15
The combination of bags of ice that Teddy can buy is
b) 6 large bags and 10 small bags
From the option b, the total number of large and small bags is greater than 15 and the total cost is 49( it doesn't exceed 50)
Answer:
Last one
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
The front elevation, side elevation, and plan of the 3D shape represent the shape C.
Answer:
4
Step-by-step explanation
The highest degree of a quadratic equation or polynomial always determine the number of factors or zeros that such polynomial have.'
For the polynomial 2x^4+6x-5
You can see that the leading degree is 4. Hence the polynomial will have 4 roots and factors
