1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
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)]

You might be interested in
PLEASE HELP ILL BRAINLIEST YOU ILL GIVE U 50 extra points
Goryan [66]
Don't trust those link my guy
7 0
2 years ago
How do you do 4x^2+3x-10=0
Likurg_2 [28]
4x^2+3x-10=0\\
4x^2+8x-5x-10=0\\
4x(x+2)-5(x+2)=0\\
(4x-5)(x+2)=0\\
x=\dfrac{5}{4} \vee x=-2

8 0
3 years ago
Bobby decided to watch all of the movies in his
disa [49]

Answer: C. y = 10x + 15

Step-by-step explanation:

He has already watched 15 movies so that's plus 15

And now he wants to watch 10 movies per week, we don't know how many weeks so that's '<em>x</em>' in this equation.

If he watches movies for <em>x </em>weeks that's 10 times <em>x </em>which is the 10x in the equation.

Hope that helped!

4 0
2 years ago
7. What is the slope of the line that passes through the pair of points (2, 5) and (8, 3)?
Nonamiya [84]

Answer:

c

Step-by-step explanation:

6 0
2 years ago
Tanya, Will, and Juan are playing a game. Juan scores 101,473 points. Tanya scores 9,879 fewer point than Juan. Will scores 9,85
Inessa05 [86]
101,473 - 9,879 = 91,594


91,594 + 9,853 = 101,447


101,447 is Will's score
8 0
3 years ago
Read 2 more answers
Other questions:
  • Which expression shows 36 + 63 as the product of their greatest common factor and the sum of two whole numbers with no common fa
    10·1 answer
  • How many zeros are in the product of any nonzero whole number and 1000?Explain your answer
    14·1 answer
  • How to justify a/b x b/c = a/c?
    13·2 answers
  • A rectangular room is 12.5 feet wide and 14 feet long. What is the perimeter of the room?
    13·2 answers
  • How do you find the distance between something. Two points, or distance in general. I'm very confused and I got I ready to do. A
    15·2 answers
  • I need help with this question
    7·1 answer
  • Can I plss have an answer on this i need it ASAP plss​
    15·1 answer
  • Lisa's father is paying for a $20 meal. He has a 15% off coupon for the meal.
    9·1 answer
  • Which expression is NOT equal to 729? 3 × 3 × 3 × 3 × 3 × 3 6,3 9 × 9 × 9 36
    15·1 answer
  • The volume of a prism is 378CM2 one of the faces are 27cm 2 the edge is x, x=?<br> mathswatch.
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!