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grandymaker [24]
3 years ago
14

Find the derivative

Mathematics
1 answer:
zalisa [80]3 years ago
6 0

First use the chain rule; take y=\dfrac{x+5}{x^2+3}. Then

\dfrac{\mathrm df}{\mathrm dx}=\dfrac{\mathrm df}{\mathrm dy}\cdot\dfrac{\mathrm dy}{\mathrm dx}

By the power rule,

f(x)=y^2\implies\dfrac{\mathrm df}{\mathrm dy}=2y=\dfrac{2(x+5)}{x^2+3}

By the quotient rule,

y=\dfrac{x+5}{x^2+3}\implies\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{(x^2+3)\frac{\mathrm d(x+5)}{\mathrm dx}-(x+5)\frac{\mathrm d(x^2+3)}{\mathrm dx}}{(x^2+3)^2}

\implies\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{(x^2+3)-(x+5)(2x)}{(x^2+3)^2}

\implies\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{3-10x-x^2}{(x^2+3)^2}

So

\dfrac{\mathrm df}{\mathrm dx}=\dfrac{2(x+5)}{x^2+3}\cdot\dfrac{3-10x-x^2}{(x^2+3)^2}

\implies\dfrac{\mathrm df}{\mathrm dx}=\dfrac{2(x+5)(3-10x-x^2)}{(x^2+3)^3}

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Which equation is correct using "is not equal to'' (≠)?
romanna [79]

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72/6=12-1=11         54-43=11

88/8=11-2=9         27-18=9

90/3=30-8=22    34-10=24

So, that makes "90 ÷ 3 − 8 _____ 34 − 10" not equal.

Hope this helps! Stay Safe!

5 0
3 years ago
What is the volume of a rectangle prism withe the base area of 24 and the height of 4​
grandymaker [24]

Answer:

The answer to your question is Volume = 32 u³

Step-by-step explanation:

Data

The volume of a rectangular prism = ?

Area of the base = 24

height = 4

Process

1.- Write the formula to calculate the volume of a pyramid

Volume = 1/3 Area of the base x height

2.- Substitution

Volume = 1/3 (24)(4)

3.- Simplification

Volume = 96/3

4.- Result

Volume = 32 u³

5 0
3 years ago
What would be the answer to this
daser333 [38]
To solve, lets convert the number so that they both have the similar exponents.

2*10^{-24} =20000*10^{-28} 



in comparing 20,000*10^-28 and 9*10^-28, we can see that one is nearly 2,000 times bigger than the other

20,000/9=2222

Answer= C
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An electronics company produces​ transistors, resistors, and computer chips. Each transistor requires 3 units of​ copper, 1 unit
Nataliya [291]
The correct answer is c
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3 years ago
58:57
IrinaK [193]

Answer: A

Step-by-step explanation: Don’t listen to Dakota he is toxic tryna ruin your life if my answer is wrong I apologize I’m just a yt tryna get more lives out there to be inspired  yt is clizey

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