Let u = x.lnx, , w= x and t = lnx; w' =1 ; t' = 1/x
f(x) = e^(x.lnx) ; f(u) = e^(u); f'(u) = u'.e^(u)
let' find the derivative u' of u
u = w.t
u'= w't + t'w; u' = lnx + x/x = lnx+1
u' = x+1 and f'(u) = ln(x+1).e^(xlnx)
finally the derivative of f(x) =ln(x+1).e^(x.lnx) + 2x
Answer:
Equivalent equations are algebraic equations that have identical solutions or roots. you can find it by adding or subtracting the same number or expression to both sides of an equation produces an equivalent equation as well as multiplying or dividing both sides of an equation by the same non-zero number produces an equivalent equation.
Step-by-step explanation:
We begin with an unknown initial investment value, which we will call P. This value is what we are solving for.
The amount in the account on January 1st, 2015 before Carol withdraws $1000 is found by the compound interest formula A = P(1+r/n)^(nt) ; where A is the amount in the account after interest, r is the interest rate, t is time (in years), and n is the number of compounding periods per year.
In this problem, the interest compounds annually, so we can simplify the formula to A = P(1+r)^t. We can plug in our values for r and t. r is equal to .025, because that is equal to 2.5%. t is equal to one, so we can just write A = P(1.025).
We then must withdraw 1000 from this amount, and allow it to gain interest for one more year.
The principle in the account at the beginning of 2015 after the withdrawal is equal to 1.025P - 1000. We can plug this into the compound interest formula again, as well as the amount in the account at the beginning of 2016.
23,517.6 = (1.025P - 1000)(1 + .025)^1
23,517.6 = (1.025P - 1000)(1.025)
Divide both sides by 1.025
22,944 = (1.025P - 1000)
Add 1000 to both sides
23,944 = 1.025P
Divide both by 1.025 for the answer
$22,384.39 = P. We now have the value of the initial investment.
Answer:
4. Find the Width by dividing 50 by 2. Then double the length, double the width, and add the products to find the perimeter = Yes
Step-by-step explanation:
The length of a rectangular dog park is 50 feet. The width is half the length.
The formula for Perimeter is given as:
P = 2L + 2W
Length = 50 feet
Width = 50 feet/2
= 25 feet
P = 2(50) + 2(25)
P = 100 + 50
P = 150 feet
Hence, writing yes or no in front of each step in the options.
1. Find the Width by dividing 50 by 2. Then add the length and width and multiply the sum to find the perimeter = No
2. Find the Width by dividing 50 by 2. Then multiply the length by the width to find the perimeter. = No
3. Find the Width by dividing 50 by 2. Then add the length and the width to find the perimeter.= No
4. Find the Width by dividing 50 by 2. Then double the length, double the width, and add the products to find the perimeter = Yes
5. Find the Width by dividing 50 by 2. Then add the sum of each length and the sum of each width to find the perimeter = No
THE CORRECT STEP IN THE ABOVE OPTION IS OPTION 4
