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swat32
3 years ago
11

Differentiating a Logarithmic Function in Exercise, find the derivative of the function. See Examples 1, 2, 3, and 4.

Mathematics
1 answer:
natulia [17]3 years ago
3 0

Answer:

g'(x)=\frac{2e^x-e^{-\frac{x}{2}}}{2(e^x+e^{-\frac{x}{2}})}

Step-by-step explanation:

We are given that a function

g(x)=ln(e^x+e^{-\frac{x}{2}})

We have to find the derivative of function

Differentiate w.r.t x

g'(x)=\frac{1}{e^x+e^{-\frac{x}{2}}}\times (e^x+e^{-\frac{x}{2}}\times (-\frac{1}{2}))

By using formula

\frac{d(lnx)}{dx}=\frac{1}{x}

\frac{d e^x}{dx}=e^x

g'(x)=\frac{e^x-\frac{e^{-\frac{x}{2}}}{2}}{e^x+e^{-\frac{x}{2}}}

Hence, the derivative function

g'(x)=\frac{2e^x-e^{-\frac{x}{2}}}{2(e^x+e^{-\frac{x}{2}})}

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Starter
4vir4ik [10]

Answer:

1) £2 = €2.32

£5 = €5.80

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2) The graph will be a straight line

3) (0, 0)

4) Label the independent variable, £ on the x-axis and dependent variable € on the y-axis

Step-by-step explanation:

1) The given conversion factors is £1 = €1.16

Therefore;

£2 = 2 × €1.16 = €2.32

£2 = €2.32

£5 = 5 × €1.16 = €5.80

£5 = €5.80

£50 = 50 × €1.16 = €58

£50 = €58

2) The shape of the plot of the directly proportional currencies graph will be a straight line

3) Given that the £ is directly proportional to the € and that the value of the € can be found directly by multiplying the amount in £ by 1.16, without the addition of a constant, the graph crosses the axes at the origin (0, 0)

4) The y-axes which is the dependent variable should be labelled €, while the x-axis which is the independent variable should be labelled £

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Answer:

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Step-by-step explanation:

The multiples of 6 are : 6, 12, 18, 24, 30, ......

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The multiples of 9 are : 9, 18, 27, 36, ......

The common multiple is 18

The least common multiple is 18

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