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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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Find z of the diagonal triangle. <br> Also, complete b.
STatiana [176]

Answer:

x = 30.91 cm , y = 29,86 cm and z = 39.30 cm.

Total area of wood = 2942.54 cm^2.

Step-by-step explanation:

sin 15 =8/x

x = 8 / sin 15

x = 30.91 cm.

and

tan 15 = 8/y

y = 8 / tan 15

= 29.86 cm.

The value of z can be found using the Pythagoras theorem:

50^2 = x^2 + z^2

z^2 =  20^2 - x^2 = 50^2 - 30.91^2

z^2 = 1554.57

z = √1554.57

=  39.30 cm.

b.  The area consists of 3 rectangles :- 1. sides x and z  2. sides z and 8 and the other has sides z and y. Also 2 triangles of height 8 and base length y cm.

Total area = 30.91  * 39.30 + 8 * 39.30 + 29.86 * 39.30 + 2 * 0.5 * 8 * 29.86

=  2942.54 cm^2.

3 0
3 years ago
Swimming speed of salmon. The graph is showed below shows the influence of the temperature T on the maximum sustainable swimming
Doss [256]

Answer:

Here we have the relation between the speed of the salmon and the temperature.

a) the relation dS/dT tell us how the speed of the salmon changes as the temperature changes, and the units should be (if speed is m/s and temperature is in °C )

[dS/dT ] = [m/s*°C ].

b) I can not do a draw of the figure, but i can give a aproximation.

For T = 18°C, we can see that we are around the maximum of the curve, this means that around this point we will find the zero in the first derivate.

then S'(18) ≈ 0 m/s*°C

this means that around this point the changes are small.

for T = 10°C

Around this region, we can see almost a linear behavior.

so we can take a range of +-2°C

S(12°C) = 25m/s

S(8°C) = 20m/s

then the slope can be obtained using the relation:

S = (Y2 - Y1)/(X2 - X1) where this is the slope for the line that goes trough the pairs. (X1, Y1) and (X2, Y2)

S = (25 - 20)/(12 - 8) = 5/4

then we have that S´(10°C) ≈ 5/4 m/s*°C

Those two results are approximations, you may find better approximations by doing this with a ruler and drawing the tangents.

5 0
3 years ago
Points W, K, and
Ksju [112]

Answer:

Points W, K, and J are collinear. Line CA and line YK intersect at point B. Point W is not contained on line m. The answers will be J,B,W

Step-by-step explanation:

Hope this helped :)

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