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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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f varies jointly as g, h, and j. One set of values is f=18, g=4, h=3, and j=5. Find f when g=5, h=12, and j=3.​
IrinaK [193]

Answer:

\boxed{60}

Step-by-step explanation:

f ∝ ghj

Convert the proportion to an equality

f = kghj

Calculate the value of k

18 = k × 4 × 3 × 5

18 = 60k

 k = ⅓

Rewrite the equation with the value of k

f = ⅓gkj

Find the new value of f

f =⅓ × 5 × 12 × 3 = \boxed{60}

6 0
3 years ago
A professor grades students on four tests, a term paper, and a final examination. Each test counts as 15% of the course grade. T
alina1380 [7]

Answer:

The Alans's average for the course is 84.5

Step-by-step explanation:

We are given

There are 4 tests, A Term paper and a Final examination.

Score = 92, 78, 82, 90.

Term paper score = 80

Final examination score = 86

Weighted mean = ∑ w.f/∑w

     also the sum of all the weights is 100% = 1

weighted mean = 15%*92 + 15%*78+15%*82+15%*90+20%*80+20%*86/1

                         = 51.3 + 33.2

                         =  84.5

Therefore the Alans's average for the course is 84.5

5 0
3 years ago
How do I solve this problem?
Papessa [141]

Answer:

there is no problem to solve here

Step-by-step explanation:

5 0
4 years ago
Read 2 more answers
What is the answer to y=x^2+6x+5
BARSIC [14]

Answer:

-5 and -1

Step-by-step explanation:

Factoring, we get y = (x+5)(x+1)

So x = -5 or -1

Or, you could've used the quadratic formula, thought it is slower.

3 0
3 years ago
Read 2 more answers
If P(A) = 0.25, then the probability of the complement of A is
djverab [1.8K]

<u>Answer:</u>

P(A') = 0.75

<u>Step-by-step explanation:</u>

We are given that the probability P(A) = 0.25 and we are to determine the probability of the complement of A.

According to the Complement Rule of any probability, the sum of the probabilities of an event and its complement must be equal to 1.

So for for the event A,

P(A) + P(A') = 1

0.25 + P(A') = 1

P(A') = 1 - 0.25

P(A') = 0.75

8 0
3 years ago
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