Write two numbers that multiply to the value on top and add to the value on bottom.<br> 42<br> 13

Solve this equation pls

Aleksandr-060686 [28]

Answer:

${ \rm{y = \frac{3 \sqrt{x} + 2x}{ {4x}^{2} } }} \\$

• We are gonna use the quotient rule

${ \boxed{ \bf{ \frac{dy}{dx} = \frac{ {\huge{v} } \frac{du}{dx} - { \huge{u}} \frac{dv}{dx} }{ {v}^{2} } }}} \\$

u is (3√x + 2x)
v is 4x²
du/dx is 3/2√x
dv/dx is 8x

• Therefore:

${ \rm{ \frac{dy}{dx} = \frac{(4 {x}^{2})( \frac{3}{2 \sqrt{x} }) - (3 \sqrt{x} + 2x)(8x) }{16 {x}^{4} } }} \\ \\ { \rm{ \frac{dy}{dx} = \frac{(6 {x}^{2})( {x}^{ - \frac{1}{2} } ) - (24 {x}^{ \frac{3}{2} } + 16 {x}^{2} ) }{16 {x}^{4} } }} \\ \\ { \rm{ \frac{dy}{dx} = \frac{ 6 {x}^{ \frac{3}{2} } - {24x}^{ \frac{3}{2} } - {16x}^{2} }{16 {x}^{4} } }} \\ \\ { \rm{ \frac{dy}{dx} = \frac{ - 18 {x}^{ \frac{3}{2} } - 16 {x}^{2} }{16 {x}^{4} } }} \\ \\ { \rm{ \frac{dy}{dx} = - 2 {x}^{ \frac{3}{2} } (9 + 8 {x}^{ \frac{4}{3} } ) \div 16 {x}^{4} }} \\ \\ { \boxed{ \boxed{ \rm{ \: \: \frac{dy}{dx} = - \frac{8 \sqrt{ {x}^{ \frac{8}{3} }} + 9}{8x {}^{ \frac{8}{3} } } \: \: }}}}$

5 0

1 year ago

Read 2 more answers

May someone please help me out on this question

NISA [10]

Answer:

A

Step-by-step explanation:

It's hard to see but when x is 6, y is 4.5. Just plug that into each equation and see which one is correct.

$x^{2} =8y\\x=6;y=4.5\\6^{2} =8(4.5)\\36=36$

8 0

2 years ago

There are two sources that serve as the foundation for conducting research on learning. The first source addresses characteristi

Leviafan [203]

Answer:

There are two sources that serve as the foundation for conducting research on learning. The first source addresses characteristics of knowledge itself and the different ways in which we learn things. The second source focuses on what goes on in our minds and how that is theoretically represented.

Step-by-step explanation:

The investigations on the process of how we learn have led to two main sources:

- Acquisition of knowledge which involves assimilation or understanding, storage and retrieval

- The second source belongs to a modern learning cognitive psychology, neuroscience, and cognitive science theories on mental representation, which concerns about the build up of an internal symbol or cognitive representation to hypothetically figure out, external reality.

8 0

2 years ago

The circle graph shows how the annual budget for a company is divided by the department. If the total annual budget is 15,000,00

Jet001 [13]

Hi if you showed a picture of the circle graph I would be happy to answer your question.

5 0

2 years ago

How much interest is earned on $2,700 in one year if it is invested at 3%?

Natalka [10]

$81 is earned by investing $2700 in one year at 3%.

3 0

2 years ago

Write two numbers that multiply to the value on top and add to the value on bottom. 42 13