This is quite a complex problem. I wrote out a really nice solution but I can't work out how to put it on the website as the app is very poorly made. Still, I'll just have to type it all in...
Okay so you need to use a technique called logarithmic differentiation. It seems quite unnatural to start with but the result is very impressive.
Let y = (x+8)^(3x)
Take the natural log of both sides:
ln(y) = ln((x+8)^(3x))
By laws of logarithms, this can be rearranged:
ln(y) = 3xln(x+8)
Next, differentiate both sides. By implicit differentiation:
d/dx(ln(y)) = 1/y dy/dx
The right hand side is harder to differentiate. Using the substitution u = 3x and v = ln(x+8):
d/dx(3xln(x+8)) = d/dx(uv)
du/dx = 3
Finding dv/dx is harder, and involves the chain rule. Let a = x+ 8:
v = ln(a)
da/dx = 1
dv/da = 1/a
By chain rule:
dv/dx = dv/da * da/dx = 1/a = 1/(x+8)
Finally, use the product rule:
d/dx(uv) = u * dv/dx + v * du/dx = 3x/(x+8) + 3ln(x+8)
This overall produces the equation:
1/y * dy/dx = 3x/(x+8) + 3ln(x+8)
We want to solve for dy/dx, achievable by multiplying both sides by y:
dy/dx = y(3x/(x+8) + 3ln(x+8))
Since we know y = (x+8)^(3x):
dy/dx = ((x+8)^(3x))(3x/(x+8) + 3ln(x+8))
Neatening this up a bit, we factorise out 3/(x+8):
dy/dx = (3(x+8)^(3x-1))(x + (x+8)ln(x+8))
Well wasn't that a marathon? It's a nightmare typing that in, I hope you can follow all the steps.
I hope this helped you :)
Answer:
The answer is "0.142466".
Step-by-step explanation:
Using the p formula for the proportion of nonconforming units through the subgrouping which can vary in sizes:
Defects 
It calculates the controls limits through the p-chart that is:
So, the upper control limits:
To make that a perfect square polynomial,
follow these steps:
1. Take the co-efficient of x term: here -16
2. Divide it by 2: -16/2 = -8
3. Square it. : (-8)^2 = 64
Thats it! 64 is the missing term you need :)
Answer:
Missing constant: 100
Step-by-step explanation:
perfect square (a - b)^2 = a^2 - 2ab + b^2
In this case
20x = 2 * x * 10
and
10^2 = 100
so
(x - 10)^2 = x^2 - 20x + 100
Answer:
Ill try to help u atleast but if i cant i can explain to u
Step-by-step explanation:
