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victus00 [196]
3 years ago
6

Use logarithmic differentiation to find the derivative with respect to x of the function y= (sin x)^lnx

Mathematics
1 answer:
Helga [31]3 years ago
4 0
Logarithmic differentiation means tAke logarithm of both sides to make the function easier to find the derivative.

y = (sinx)^lnx

ln(y) = ln((sinx)^lnx)

power rule logarithm

ln(y) = ln(x) ln(sinx)

Take derivative

y'/y = ln(sinx)(1/x) + ln(x) cosx/sinx

multiply both sides by y

y' = y( ln(sinx)/x + ln(x)cotx )

remember y = (sinx)^lnx
sub this in for y

y' = (ln(sinx)/x + ln(x)cotx)(sinx)^lnx
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Consider a collection of envelopes consisting of 2 red envelopes​, 2 blue envelopes​, 2 green envelopes​, and 3 yellow envelopes
77julia77 [94]

The probability that all three randomly selected envelopes are yellow without replacement is 1/84.

<h3>What is a combination?</h3>

It is an arrangement of a set of numbers from a total set where the order of the set is not relevant.

We have,

2 red envelopes​

2 blue envelopes​

2 green envelopes​

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The probability that all three randomly selected envelopes are yellow without replacement.

= \frac{^3C_1}{^9C_1} \frac{^2C_1}{^8C_1} \frac{^1C_1}{^7C_1}

= (3/9) x (2/8) x (1/7)

= (3x2x1)/(9x8x7)

= 1/84

Thus,

The probability that all three randomly selected envelopes are yellow without replacement is 1/84.

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brainly.com/question/14355408

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