Answer:
Step-by-step explanation:
We are given that:
And we want to find F'(0).
First, find F(x):
![\displaystyle F'(x) = \frac{d}{dx}\left[ f(3x)]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20F%27%28x%29%20%3D%20%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft%5B%20f%283x%29%5D)
From the chain rule:
![\displaystyle \begin{aligned} F'(x) &= f'(3x) \cdot \frac{d}{dx} \left[ 3x\right] \\ \\ &= 3f'(3x)\end{aligned}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cbegin%7Baligned%7D%20F%27%28x%29%20%26%3D%20f%27%283x%29%20%5Ccdot%20%5Cfrac%7Bd%7D%7Bdx%7D%20%5Cleft%5B%203x%5Cright%5D%20%5C%5C%20%5C%5C%20%26%3D%203f%27%283x%29%5Cend%7Baligned%7D)
Then:
In conclusion, F'(0) = 15.
Answer:
Step-by-step explanation:
interchange x and y
y= 1/(x - 2)
x = 1 / (y - 2) Multiply both sides by y - 2
x(y - 2) = 1 Remove the brackets
xy - 2x = 1 Add x to both sides
xy = 1 + 2x Divide by x
y = (1 + 2x)/x
The brackets have been destroyed. The answer is as I've given it.
y = (1/x) + 2
Answer:
initial value is 21
Step-by-step explanation:
y=mx+b
6= -3(5) +b
b=21
Answer:
Leila is buying a dinosaur model. The price of the model is xxx dollars, and she also has to pay a 7\%7%7, percent tax.
Which of the following expressions could represent how much Leila pays in total for the model?
Step-by-step explanation:
The original price of the dinosaur model is "x" dollars
On top of that, the sales tax is 7% of the original price
Hence,
The total price would be the original amount PLUS the taxed amount
Original Amount = x
Taxed Amount = 7% of x
That is, 7% in decimal multiplied with "x".
7/100 = 0.07
0.07 * x = 0.07x
Total amount = x + 0.07x = 1.07x
The expression for total amount is 1.07x
Answer:
x=2 : )
Step-by-step explanation:
4(3x-1)=20
12x-4=20
12x=24
x=2
