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sergij07 [2.7K]
3 years ago
8

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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Answer:

10x - 5

Step-by-step explanation:

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5 0
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What is the numeric value of E + B?​
ivanzaharov [21]

Answer:

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Step-by-step explanation:

Also, when it's converted to number I.e.

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Answer:

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Step-by-step explanation:

8 0
3 years ago
You bought your current house 10 years ago for £55,000. There are currently three similar properties for sale on your street. Pr
galben [10]

Answer:

<u>The house could be sold between £ 77,000 and £ 79,500</u>

Step-by-step explanation:

Cost of the house = £ 55,000

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Suggested price with at least 40% profit = £ 55,000 + £ 22,000

<u>Suggested price with at least 40% profit = £ 77,000</u>

Properties price on the same street:

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Property 3 £83,500

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Mean of these prices = 238,500 / 3

<u>Mean of these prices = £ 79,500</u>

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Answer:

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