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 ride took 7 1/2 hours to complete.
Step-by-step explanation:
If the bicyclist is going at a constant speed of 6mi/hr it would take 7 1/2 hours to ride 45 miles.
6*7 1/2=45
596*25%=149
149 people over the age of 65 years old voted
A book is sold in Belize for 80.39 Belize dollars.
In Brazil, it sells for 63.65 Brazilian reals.
The exchange rate of US Dollars to Belize Dollars is 1:1.9246
<span>The exchange rate of US Dollars to Brazilian Real is 1:1.7880
</span>
If we convert the two into dollars,
Belize Dollars
1 : 1.9246 = X : <span>80.39
1.9246X = 80.39
X = $ 41.77
</span>Brazilian Real
1 : 1.7880 = X : 63.65 <span>
</span>1.7880X = 63.65 <span>
X = $ 35.60
</span>
Difference = $ 41.77 - $ 35.60
Difference = $ 6.17
<span>So, in Belize the book is more expensive by $ 6.17</span>
Answer:
7
Step-by-step explanation:
if you meant hundredths it would be 9, but 7 is in the hundreds place
