Please help me find the cost **marking brainliest** and may you please show your work :)

Differentiate y=x⁴(1-2x⁵)⁶(5-8x³)².

Liula [17]

Step-by-step explanation:

Let $y(x)=f(x)g(x)h(x)$ where

$f(x) = x^4$

$g(x)= (1 -2x^5)^6$

$h(x)= (5 - 8x^3)^2$

so that

$y(x) = x^4(1 -2x^5)^6(5 - 8x^3)^2$

Recall that the derivative of the product of functions is

$y'(x)=f'(x)g(x)h(x)+f(x)g'(x)h(x)+f(x)g(x)h'(x)$

so taking the derivatives of the individual functions, we get

$f'(x) = 4x^3$

$g'(x) = 6(1 - 2x^5)^5(-10x^4)$

$h'(x) = 2(5 - 8x^3)(-24x^2)$

So the derivative of y(x) is given by

$y'(x) = 4x^3(1 -2x^5)^6(5 - 8x^3)^2 + x^4 6(1 -2x^5)^5(-10x^4)(5 - 8x^3)^2 + x^4(1 -2x^5)^6 2(5 - 8x^3)(-24x^2)$

or

$y'(x) = 4x^3(1 -2x^5)^6(5 - 8x^3)^2$

$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:- 60x^8(1 -2x^5)^5(5 - 8x^3)^2$

$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:- 48x^6(1 -2x^5)^6 2(5 - 8x^3)$

3 0

2 years ago

Which piecewise function is shown in the graph?

mash [69]

Based on the characteristics of linear and piecewise functions, the piecewise function $f(x) = \left \{ {{-0.5\cdot x +1, \,x < 0} \atop {2\cdot x - 2, \,x \ge 0}} \right.$ is shown in the graph attached herein. (Correct choice: A)

<h3>How to determine a piecewise function</h3>

In this question we have a graph formed by two different linear functions. Linear functions are polynomials with grade 1 and which are described by the following formula:

y = m · x + b (1)

Where:

x - Independent variable.
y - Dependent variable.
m - Slope
b - Intercept

By direct observation and by applying (1) we have the following piecewise function:

$f(x) = \left \{ {{-0.5\cdot x +1, \,x < 0} \atop {2\cdot x - 2, \,x \ge 0}} \right.$

Based on the characteristics of linear and piecewise functions, the piecewise function $f(x) = \left \{ {{-0.5\cdot x +1, \,x < 0} \atop {2\cdot x - 2, \,x \ge 0}} \right.$ is shown in the graph attached herein. (Correct choice: A)

To learn more on piecewise functions: brainly.com/question/12561612

#SPJ1

3 0

1 year ago

2. If the data in the table were displayed in a circle graph, which percent would NOT appear in the graph? Round to the nearest

german

Adding the numbers gives us a total of 65

Jan = 20/65 = 30.7% = 31%
Feb = 25/65 = 38.4% = 38%
Mar = 1/65 = 1.5% = 2%
Apr = 3/65 = 4.6% = 5%
May = 16/65 = 24.6% = 25%

I believe ur answer is 30%

6 0

2 years ago

Can y’all please help me answer these questions

mario62 [17]

Step-by-step explanation:

4.

⇒ $V = \pi r^{2}h$

⇒ $V = \pi(10)^{2}(40)$

⇒ $V = 4000\pi$

⇒ $V = 12566.4cm^{3}$

5.

⇒ $V = \frac{1}{3}\pi r^{2}h$

⇒ $V = \frac{1}{3}\pi (8)^{2}(h)$

As we know the radius and slant height, we can use Pythagoras' Theorem to find the perpendicular height.

⇒ $a^{2} + b^{2} = c^{2}$

⇒ $(8)^{2} + h^{2} = 20^{2}$

⇒ $h = \sqrt{20^{2} - 8^{2}}$

⇒ $h = 4\sqrt{21}$

Now substitute this into the volume formula.

⇒ $V = \frac{1}{3}\pi (8)^{2}(4\sqrt{21})$

⇒ $V = \frac{256\sqrt{21} }{3}\pi$

⇒ $V = 1228.5mm^{3}$

6.

⇒ $V = l^{3}$

⇒ $V = (3.1)^{3}$

⇒ $V = 29.8inches^{3}$

7.

⇒ $V = \frac{1}{3}lwh$

⇒ $V = \frac{1}{3}(12)(4)(6)$

⇒ $V = 96inches^{3}$

6 0

2 years ago

Read 2 more answers

How are radicals and rational exponents related?

icang [17]

Answer:

Any radical in the form can be written using a fractional exponent in the form . The relationship between and works for rational exponents that have a numerator of 1 as well. For example, the radical can also be written as , since any number remains the same value if it is raised to the first power.

Step-by-step explanation:

8 0

2 years ago

Please help me find the cost **marking brainliest**and may you please show your work :)

Please help me find the cost marking brainliestand may you please show your work :)