All categories

2 years ago

Y=(2x-3)^5(2-x^4)^3 differentiate the function please

1 answer:

5 0

$\bf y=(2x-3)^5(2-x^4)^3\\\\
-------------------------------\\\\
\cfrac{dy}{dx}=\stackrel{\textit{product rule}}{[5(2x-3)^4\cdot 2(2-x^4)3]~~+~~[(2x-3)^5[3(2-x^4)^2(-4x^3)]]}
\\\\\\
\cfrac{dy}{dx}=10(2x-3)^4(2-x^4)^3~~-~~12x^3(2x-3)^5(2-x^4)^2
\\\\\\
\cfrac{dy}{dx}=\stackrel{\textit{common factor}}{2(2x-3)^4(2-x^4)^2}~[5(2-x^4)-6x^3(2x-3)]
\\\\\\
\cfrac{dy}{dx}=2(2x-3)^4(2-x^4)^2~[10-5x^4-12x^4+18x^3]
\\\\\\
\cfrac{dy}{dx}=2(2x-3)^4(2-x^4)^2(10-17x^4+18x^3)$

You might be interested in

Solve the system of equation by elimination. <br> 6x-3y=-21<br> 4x=3y-9

dedylja [7]

2x=-12 simplified, the expression or solving for X would be X=-6

5 0

2 years ago

_____ less than a number is 51

Kryger [21]

Answer:

W number - blank is 51.

Step-by-step explanation:

I don't understand what the question is. What is the number unless you want something random then here:

Blank - 52

a number = 1

52 - 1 = 51

3 0

2 years ago

Valerie is performing an experiment by spinning a metal weight around on the end of a nylon thread. How far does the metal weigh

Triss [41]

Answer:

35.6 m

Step-by-step explanation:

Number of revolutions = 40

Length of thread = 0.89 m

Total Distance = Number of revolutions * Length of Thread

Total Distance = 40 * 0.89 = 35.6 m

3 0

2 years ago

True or false ? I’m the deductive thinking you formulate general ideas and rules based on your experiences and observations

kicyunya [14]

Answer:The answer is False. i hope i helped you out

5 0

2 years ago

Read 2 more answers

It takes the hot water faucet twice as long to fill a bathtub as it does the cold water faucet. Left on together, the cold and h

Lerok [7]

Answer:

Step-by-step explanation:

Make a system of equations

Give the hot and cold faucets variables

Set x to be the minutes it takes for the hot water faucet to fill up the tub and Set y to be the minutes it takes for the cold water faucet to fill up the tub

She first equation is x = 2y because the hot faucet takes <em>2 times</em> as much time as the cold water

The second equation is x + y = 5 because if you add the number of minutes each takes to fill a tub, it will add up to 5 minutes

Now you have the equations

x = 2y

x + y = 5

So you can plug the first equation in for x in the second one to make

2y + y = 5

which equals 3y = 5

Then you divide 3 from both sides to get

y = $\frac{5}{3}$

Since y is the number of minutes the cold water faucet takes to fill the tub, then the cold faucet takes $\frac{5}{3}$ minutes for the cold water faucet to fill the tub itself

8 0

2 years ago