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Nikolay [14]
3 years ago
9

Find dy/dx (derivative) using Implicit Differentiation: xe^y=x-y

Mathematics
1 answer:
miss Akunina [59]3 years ago
6 0
D (xe^y)/dx = d(x - y)dx
(e^y)dx/dx + xd(e^y)/dx = 1 - y'
e^y + xy'e^y = 1 - y'
(1 + xe^y)y' = 1 - e^y
y' = (1 - e^y)/(1 + xe^y)
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Step-by-step explanation:

125,000×1.05⁷ ≈ 175,888

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The ratio 5:20 written as a fraction​
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<em> </em><em>1</em><em>:</em><em>4</em>

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Two consecutive negative integers have a product of 30. what are the integers?
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The function f(t)=-16 + 100 models the height of a ball, in feet, dropped from a 100-foot rooftop at time t, in seconds.
Mazyrski [523]

Using it's concept, it is found that the average rate of change of the function during the interval from 0 to 2 seconds is given by:

B. -32 ft/s; the average change in altitude of the ball each second over that interval.

<h3>What is the average rate of change of a function?</h3>

The average rate of change of a function is given by the change in the output divided by the change in the input. Hence, over an interval [a,b], the rate is given as follows:

r = \frac{f(b) - f(a)}{b - a}

In this problem, the function is given by:

f(t) = -16t² + 100.

The outputs are given as follows:

  • f(0) = -16(0)² + 100 = 100.
  • f(0) = -16(2)² + 100 = 36.

Hence the average rate of change is given by:

r = (36 - 100)/(2 - 0) = -32 ft/s.

And the correct option is:

B. -32 ft/s; the average change in altitude of the ball each second over that interval.

More can be learned about the average rate of change of a function at brainly.com/question/24313700

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8 0
1 year ago
Given that <img src="https://tex.z-dn.net/?f=a%5Cneq%20b" id="TexFormula1" title="a\neq b" alt="a\neq b" align="absmiddle" class
xz_007 [3.2K]

Answer:

Step-by-step explanation:

√a+√b=√(a+b)

squaring

a+b+2√a√b=a+b

or 2√a√b=0

which is possible only if a=0 or b=0

Both a and b can't be zero as a≠b

8 0
3 years ago
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