All categories

3 years ago

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)]

You might be interested in

Examine the system of equations.

MrMuchimi

answer:

$x = - 2 \\ y = 2 \\ \\ ( - 2, \: 2)$

explanation:

$y = - \frac{1}{2} x + 1 \\ y = 2x + 6 \\ first \: equation \: add \: \frac{1}{2} from \: both \\ sides \\ \\ second \: equation \: subtract \: 2x \: from \\ both \: sides \\ \\ y + \frac{1}{2} x = 1 \\ y - 2x = 6 \\ solve \: the \: first \: equation \\ \\ y + \frac{1}{2} x = 1 \\ subtract \: \frac{x}{2} from \: both \: sides \\ \\ y = - \frac{1}{2} x + 1 \\ substitute \: - \frac{x}{2} + 1 \: for \: y \: in \: the \\ other \: equation \\ \\ - \frac{1}{2} x + 1 - 2x = 6 \\ add \: \frac{1}{2} x \: to \: 2x \\ \\ - \frac{5}{2} x + 1 = 6 \\ subtract \: 1 \: from \: both \: sides \\ \\ - \frac{5}{2} x = 5 \\ divide \: both \: sides \: by \: - \frac{5}{2} \\ \\ x = - 2 \\ substitute \: the \: value \: of \: x \: into \\ an \: equation \\ \\ y = - \frac{1}{2} ( - 2) + 1 \\ distribute \\ \\ y = 1 + 1 \\ add \\ \\ y = 2 \\ \\ ( - 2, \: 2)$

7 0

3 years ago

A Statistics class is estimating the mean height of all female students at their college. They collect a random sample of 36 fem

Butoxors [25]

Answer: = ( 63.9, 66.7)

Therefore at 90% confidence interval (a,b)= ( 63.9, 66.7)

Step-by-step explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

x+/-zr/√n

Given that;

Mean x = 65.3

Standard deviation r = 5.2

Number of samples n = 36

Confidence interval = 90%

z(at 90% confidence) = 1.645

Substituting the values we have;

65.3 +/-1.645(5.2/√36)

65.3 +/-1.645(0.86667)

65.3+/- 1.4257

65.3+/- 1.4

= ( 63.9, 66.7)

Therefore at 90% confidence interval (a,b)= ( 63.9, 66.7)

4 0

3 years ago

Please help! It's due soon.

Sedbober [7]

Answer:

Because f(g(x)) = g(f(x)) = x, f and g <u>are </u> inverse functions.

Step-by-step explanation:

f(g(x)) = f( $\frac{1}{4}\sqrt{x}$ ) = $16(\frac{1}{4}\sqrt{x} ) ^{2} = 16(\frac{1}{16}x)=x$

g(f(x)) = g $(16x^{2}) = \frac{1}{4}\sqrt{16x^{2} } = \frac{1}{4}(4x) = x$

6 0

3 years ago

Jodi bought a new sofa for $1,430, including finance charge. She made down payment of $130 and paid off the balance in 18 months

m_a_m_a [10]

The finance Charge would be $140. you would multiply 18 by 80 and then add the 130 and take that number and subtract the 1,430

6 0

3 years ago

A village lost 15% of its cows in a flood and 10% of the remainder died of

Free_Kalibri [48]

Answer:

10000 cows.

Step-by-step explanation:

Remainder before the 10% loss: (7650/9) x 10 = 8500

Total before any losses : (8500/85) x 100 = 10000

7 0

3 years ago