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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)]

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Answer:

$\rm - \dfrac{11}{2}$

Step-by-step explanation:

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Step-by-step explanation

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Step-by-step explanation:

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What is true about the completely simplified sum of the polynomials 3x2y2 − 2xy5 and −3x2y2 + 3x4y?

Elanso [62]

Answer:

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Step-by-step explanation:

we have

(3x^{2}y^{2}-2xy^{5})+(-3x^{2}y^{2}+3x^{4}y)

Group terms that contain the same variable

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3 years ago

Read 2 more answers