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3 years ago

100 POINTS PLEASE PROVIDE STEPS FIND FIRST DERIVATIVE AND SIMPLIFY ANSWER

Mathematics

2 answers:

BaLLatris [955]3 years ago

5 0

Answer:

h'(x) = (-x² ln x + x² + 1) / (x (x² + 1)^(³/₂))

Step-by-step explanation:

h(x) = ln x / √(x² + 1)

You can either use quotient rule, or you can rewrite using negative exponents and use product rule.

h(x) = (ln x) (x² + 1)^(-½)

h'(x) = (ln x) (-½) (x² + 1)^(-³/₂) (2x) + (1/x) (x² + 1)^(-½)

h'(x) = (-x ln x) (x² + 1)^(-³/₂) + (1/x) (x² + 1)^(-½)

h'(x) = (x² + 1)^(-³/₂) (-x ln x + (1/x) (x² + 1))

h'(x) = (1/x) (x² + 1)^(-³/₂) (-x² ln x + x² + 1)

h'(x) = (-x² ln x + x² + 1) / (x (x² + 1)^(³/₂))

dimaraw [331]3 years ago

3 0

Solution:

h(x) = ln(x)/√x^2+1

h(x) = ln(x) * (x^2 + 1)^-1/2

h(x) = ln(x) * (-1/2) * (x^2 + 1)^-3/2 * 2x + 1/x * (x^2 + 1)^-1/2

h(x) = -x ln(x) * (x^2 + 1)^-3/2 + 1/x * (x^2 + 1)^-1/2

h(x) = (x^2 + 1)^-3/2 * (-x ln(x) + 1/x * (x^2 + 1))

h(x) = -x^2ln(x)+x^2+1/(x(x^2+1)^3/2)

Best of Luck!

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masha68 [24]

Answer:

(2,20)

Step-by-step explanation:

The given function is

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For the first point we substitute x=3 and f(x)=250

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$20= 2 \cdot \: {5}^{2} \\ 20 = 2 \times 25 \\ 20 = 50$

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$50= 2 \cdot \: {5}^{2} \\ 50 = 2 \times 25 \\ 50 = 50$

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3 years ago

AB is parallel to CD,<br> a) Find the value of angle x.<br> b) work out the value of angle y.

anastassius [24]

Answer:

x=69° y=69°

Step-by-step explanation:

Angle x is an alternate angle so it is equal to the angle above it (69)

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One ballispicked at random from a box containing 3redballs and 1green balls. If X is the number of redballs picked, find the pro

Paladinen [302]

Answer:

P(X = 0) = 0.25

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Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

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3 red balls out of 4, one picked, so we can have either 0 red balls or 1 red ball. The probability disitribution is the probability of each outcome.

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3 years ago

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Bess [88]

Answer:

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Step-by-step explanation:

The height, h (in meters), of the object launched from a platform is represented by the equation

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Substitute $x=0$ to find the height:

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a standard deck of cards missing the queen of hearts in the 2 of clubs what is the probability of pulling either an ace or a spa

Butoxors [25]

<h3>Answer: 8/25</h3>

=======================================================

Explanation:

In a standard deck, there are 52 cards.

If this deck is missing the queen of hearts and 2 of clubs, then we really have 52-2 = 50 cards in the deck.

There are 4 aces and 13 spades. Those values add to 4+13 = 17, but we need to subtract off 1 to account for the ace of spades counted twice. We have 17-1 = 16 cards that are either an ace, a spade, or both.

Or you can think of it like saying 13 spades + 1 ace of hearts + 1 ace of diamonds + 1 ace of clubs = 16 cards total.

-----------------

The event space has A = 16 cards in it, while the sample space has B = 50 cards.

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