Step-by-step explanation:
Let
where
![f(x) = x^4](https://tex.z-dn.net/?f=f%28x%29%20%3D%20x%5E4)
![g(x)= (1 -2x^5)^6](https://tex.z-dn.net/?f=g%28x%29%3D%20%281%20-2x%5E5%29%5E6)
![h(x)= (5 - 8x^3)^2](https://tex.z-dn.net/?f=h%28x%29%3D%20%285%20-%208x%5E3%29%5E2)
so that
![y(x) = x^4(1 -2x^5)^6(5 - 8x^3)^2](https://tex.z-dn.net/?f=y%28x%29%20%3D%20x%5E4%281%20-2x%5E5%29%5E6%285%20-%208x%5E3%29%5E2)
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)](https://tex.z-dn.net/?f=y%27%28x%29%3Df%27%28x%29g%28x%29h%28x%29%2Bf%28x%29g%27%28x%29h%28x%29%2Bf%28x%29g%28x%29h%27%28x%29)
so taking the derivatives of the individual functions, we get
![f'(x) = 4x^3](https://tex.z-dn.net/?f=f%27%28x%29%20%3D%204x%5E3)
![g'(x) = 6(1 - 2x^5)^5(-10x^4)](https://tex.z-dn.net/?f=g%27%28x%29%20%3D%206%281%20-%202x%5E5%29%5E5%28-10x%5E4%29)
![h'(x) = 2(5 - 8x^3)(-24x^2)](https://tex.z-dn.net/?f=h%27%28x%29%20%3D%202%285%20-%208x%5E3%29%28-24x%5E2%29)
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)](https://tex.z-dn.net/?f=y%27%28x%29%20%3D%204x%5E3%281%20-2x%5E5%29%5E6%285%20-%208x%5E3%29%5E2%20%2B%20%20x%5E4%206%281%20-2x%5E5%29%5E5%28-10x%5E4%29%285%20-%208x%5E3%29%5E2%20%2B%20%20x%5E4%281%20-2x%5E5%29%5E6%202%285%20-%208x%5E3%29%28-24x%5E2%29)
or
![y'(x) = 4x^3(1 -2x^5)^6(5 - 8x^3)^2](https://tex.z-dn.net/?f=y%27%28x%29%20%3D%204x%5E3%281%20-2x%5E5%29%5E6%285%20-%208x%5E3%29%5E2)
![\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:- 60x^8(1 -2x^5)^5(5 - 8x^3)^2](https://tex.z-dn.net/?f=%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A-%2060x%5E8%281%20-2x%5E5%29%5E5%285%20-%208x%5E3%29%5E2)
![\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:- 48x^6(1 -2x^5)^6 2(5 - 8x^3)](https://tex.z-dn.net/?f=%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A-%2048x%5E6%281%20-2x%5E5%29%5E6%202%285%20-%208x%5E3%29)
Simplify,,,,,,,,,,,,,,,,,,,
tatuchka [14]
It is D , if you plus into a calculator it simplifies for you !!
Answer:
hello,
Step-by-step explanation:
a)
In an isocele triangle, base's angles have the measure:
42+2a=180
2a=180-42
a=69(°)
b)
in a triangle, an external angle has for measure the sum of the angles not adjacents.
55+b=132
b=77 (°)
c)
in a quadrilater the sum of the (interior) angles is 2*180=360 degrees.
90+90+68+c=360
c=360-90-90-68
c=112 (°)
30% = .3
.3(24.40a + 14.50c)
24.40 = cost of adult ticket
14.50 = cost of child ticket
a = # of adult tickets sold
c = # of child tickets sold
.3 * 24.40a + .3 * 14.50c
answer: 7.32a + 4.35c