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Natasha_Volkova [10]
3 years ago
11

Use logarithmic differentiation to find dy/dx if y=(cosx)sinx. Write the derivative in terms of x only. Show all your work.

Mathematics
2 answers:
gladu [14]3 years ago
7 0

Step-by-step explanation:

y = (cos x)^(sin x)

Take log both sides.

ln y = ln ((cos x)^(sin x))

ln y = (sin x) ln (cos x)

Take derivative.

1/y dy/dx = (sin x) (1/cos x) (-sin x) + (cos x) ln (cos x)

dy/dx = y [ (cos x) ln (cos x) − sin x tan x ]

dy/dx = (cos x)^(sin x) [ (cos x) ln (cos x) − sin x tan x ]

Your answer is correct.

andriy [413]3 years ago
6 0

Answer:

[(cosx)^(sinx)][-sinx(tanx) + (cosx)ln(cosx)]

Step-by-step explanation:

y = (cosx)^(sinx)

lny = (sinx) × ln(cosx)

(1/y)×dy/dx = (sinx)(1/cosx)(-sinx) + (cosx)ln(cosx)

(1/y)dy/dx = -sinxtanx + (cosx)ln(cosx)

dy/dx = y[-sinxtanx + (cosx)ln(cosx)]

dy/dx =

[(cosx)^(sinx)][-sinxtanx + (cosx)ln(cosx)]

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Answer:

I will need 26.4 pounds of the expensive nuts and 1.6 pounds of the cheap nuts.

Step-by-step explanation:

Since I have one type of nut that sells for $ 4.50 / lb and another type of nut that sells for $ 8.00 / lb, and I would like to have 28 lbs of a nut mixture that sells for $ 7.80 / lb, to determine how much of each nut will I need to obtain the desired mixture, the following calculation must be performed:

8 x 0.95 + 4.5 x 0.05 = 7.825

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0.94 x 28 = 26.32

26.4 x 8 + 1.6 x 4.5 = 218.4

218.4 / 28 = 7.8

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Step-by-step explanation:

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