The derivatives for this problem are given as follows:
a) ![f^{\prime}(x) = -4\sin{x} + \frac{1}{x + 1}](https://tex.z-dn.net/?f=f%5E%7B%5Cprime%7D%28x%29%20%3D%20-4%5Csin%7Bx%7D%20%2B%20%5Cfrac%7B1%7D%7Bx%20%2B%201%7D)
b)
.
<h3>What is the derivative of the sum?</h3>
The derivative of the <u>sum is the sum of the derivatives</u>.
In this problem, the function is:
![f(x) = 4\cos{x} + \ln{(x + 1)}](https://tex.z-dn.net/?f=f%28x%29%20%3D%204%5Ccos%7Bx%7D%20%2B%20%5Cln%7B%28x%20%2B%201%29%7D)
Using a derivative table for the derivatives of the cosine and the ln, the derivative of the function is:
![f^{\prime}(x) = (4\cos{x})^{\prime} + (\ln{(x + 1)})^{\prime}](https://tex.z-dn.net/?f=f%5E%7B%5Cprime%7D%28x%29%20%3D%20%284%5Ccos%7Bx%7D%29%5E%7B%5Cprime%7D%20%2B%20%28%5Cln%7B%28x%20%2B%201%29%7D%29%5E%7B%5Cprime%7D)
![f^{\prime}(x) = -4\sin{x} + \frac{1}{x + 1}](https://tex.z-dn.net/?f=f%5E%7B%5Cprime%7D%28x%29%20%3D%20-4%5Csin%7Bx%7D%20%2B%20%5Cfrac%7B1%7D%7Bx%20%2B%201%7D)
What is the product rule?
The derivative of the product is given as follows:
![(f(x) \times g(x))^{\prime} = f^{\prime}(x)g(x) + g^{\prime}(x)f(x)](https://tex.z-dn.net/?f=%28f%28x%29%20%5Ctimes%20g%28x%29%29%5E%7B%5Cprime%7D%20%3D%20f%5E%7B%5Cprime%7D%28x%29g%28x%29%20%2B%20g%5E%7B%5Cprime%7D%28x%29f%28x%29)
In this problem, we have that:
.
.
Hence the derivative is:
.
More can be learned about derivatives at brainly.com/question/2256078
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Answer:
360-(124+124)= 360-248=122 divided by 4=30.5
Answer:
X + 45
X + 12
1 - x
X - 13
Step-by-step explanation:
Using the keywords sum of, more than, and subtracted will help you. (You can also flip the expression since it didn't say how.
Answer:
5
Step-by-step explanation:
Penta -5
gon means many sides
Answer:
At 1:40 pm you will reach the market.
Step-by-step explanation:
Distance (d) = 11 km
Average speed (v) = 3 km/h
Formula:
![\rm Average \: speed = \dfrac{Distance}{Time} \\ \\ \rm 3 = \dfrac{11}{t} \\ \\ \rm t = \dfrac{11}{3} \\ \\ \rm t = 3 \frac{2}{3} \\ \\ \rm t = 3 hr \: 40min](https://tex.z-dn.net/?f=%20%5Crm%20Average%20%20%5C%3A%20speed%20%3D%20%5Cdfrac%7BDistance%7D%7BTime%7D%20%5C%5C%20%20%5C%5C%20%20%5Crm%203%20%3D%20%20%5Cdfrac%7B11%7D%7Bt%7D%20%20%5C%5C%20%20%5C%5C%20%20%5Crm%20t%20%3D%20%20%5Cdfrac%7B11%7D%7B3%7D%20%20%5C%5C%20%20%5C%5C%20%20%5Crm%20t%20%3D%203%20%5Cfrac%7B2%7D%7B3%7D%20%20%5C%5C%20%20%5C%5C%20%20%5Crm%20t%20%3D%203%20hr%20%5C%3A%2040min)
It will take 3 hours 40 minutes to reach the market.
So, if you set off for the market at 10 am you will reach market by 1:40 pm (10 am + 3hr 40min).