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Rama09 [41]
4 years ago
10

Differentiating Exponential functions In Exercise,find the derivative of the function. See Example 2 and 3.

Mathematics
1 answer:
Bess [88]4 years ago
7 0

Answer:

\frac{d}{dx} (e^{1-x}) = e^{1-x} (-1) = -e^{1-x}

Step-by-step explanation:

Assuming the following function y = e^{1-x}} we want to find the derivate of this function.

For this case we need to apply the chain rule given by the following formula:

\frac{df(u)}{dx} = \frac{df}{du} \frac{du}{dx}

On this case our function is f = e^u and our value for u is u =1-x

If we appply this rule we got this:

\frac{df(u)}{dx} = \frac{d}{du} (e^u) \frac{d}{dx} (1-x)

\frac{df(u)}{dx} = e^u (-1)

And now w can substitute u = 1-x and we got:

\frac{d}{dx} (e^{1-x}) = e^{1-x} (-1) = -e^{1-x}

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1. Regina. Phil and Joseph each wrote expressions to represent their hourly
aleksandrvk [35]

Answer:

15

Step-by-step explanation:

Regina: 6.5h

Phil: 3(2.5h+5)

When you plug in the number of hours, you get the weekly pay.  In order to get the same weekly pay, set the equations equal to each other.

6.5h=3(2.5h+5), This is an equation to find the number of hours it will take for them to get equal pay. Now, simplify.

6.5h=7.5h+15

-h=15

h=-15, -15 hours is your answer. You can't work negative hours though which means that Regina and Phil will never be able to make the same amount.

Phil has a higher rate and starting value, this means that Regina will never make the same amount working the same hours.

6 0
3 years ago
Ratio Question;
SashulF [63]

*Given

Money of Phoebe            - 3 times as much as Andy

Money of Andy                - 2 times as much as Polly

Total money of Phoebe,  - £270

   Andy and Polly

*Solution

Let

B - Phoebe's money

A - Andy's money

L - Polly's money

1. The money of the Phoebe, Andy, and Polly, when added together would total £270. Thus,

                 B + A + L  = £270                     (EQUATION 1)

2. Phoebe has three times as much money as Andy and this is expressed as

 

                 B = 3A

3. Andy has twice as much money as Polly and this is expressed as

                 A = 2L                           (EQUATION 2)

4. This means that Phoebe has ____ as much money as Polly,

                B = 3A

                B = 3 x (2L)

                B = 6L                            (EQUATION 3)

This step allows us to eliminate the variables B and A in EQUATION 1 by expressing the equation in terms of Polly's money only.

5. Substituting B with 6L, and A with 2L, EQUATION 1 becomes,

                 6L + 2L + L = £270

                               9L = £270

                                 L = £30

So, Polly has £30.

6. Substituting L into EQUATIONS 2 and 3 would give us the values for Andy's money and Phoebe's money, respectively.

                 A = 2L                          

                 A = 2(£30)

                 A = £60

Andy has £60

                 B = 6L                        

                 B = 6(£30)

                 B = £180

Phoebe has £180

Therefore, Polly's money is £30, Andy's is £60, and Phoebe's is £180.

3 0
3 years ago
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Each of the 13 members of a basketball team bought a team emblem. The emblems cost the team 78 dollars. How much did it cost eac
Irina-Kira [14]

Answer:

$6

Step-by-step explanation:

78/13=6

6 0
4 years ago
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Step-by-step explanation:

Geometric mean is the square root of the product.

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