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3 years ago

Solve this derivative using the quotient rule

Mathematics

1 answer:

LekaFEV [45]3 years ago

7 0

$\bf y=\cfrac{(-x+5)^5}{3x-4}\implies y=\cfrac{(5-x)^5}{3x-4}
\\\\\\
\cfrac{dy}{dx}=\stackrel{quotient~rule}{\cfrac{5(5-x)^4(-1)(3x-4)~~-~~(5-x)^5(3)}{(3x-4)^2}}
\\\\\\
\cfrac{dy}{dx}=\cfrac{-5(5-x)^4(3x-4)-3(5-x)^5}{(3x-4)^2}
\\\\\\
\cfrac{dy}{dx}=\cfrac{\stackrel{common~factor}{-(5-x)^4}[5(3x-4)+3(5-x)]}{(3x-4)^2}
\\\\\\
\cfrac{dy}{dx}=\cfrac{-(5-x)^4~~[15x-20+15-3x]}{(3x-4)^2}
\\\\\\
\cfrac{dy}{dx}=\cfrac{-(5-x)^4~~[12x-5]}{(3x-4)^2}\implies \cfrac{dy}{dx}=\cfrac{(5-x)^4~~[5+12x]}{(3x-4)^2}$

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Please help! I attached the question below.

kompoz [17]

Answer:

$\frac{2(c+2)}{c(c-2)}$

Step-by-step explanation:

$\frac{c^{2}-4 }{6c^{4}+15c^{3}}=\frac{(c-2)(c+2)}{c(6c^{3}+15c^{2}) }$

Identity used:

$a^{2}-b^{2}=(a-b)(a+b)$

$\frac{c^{2}-4c+4}{12c^{3}+30c^{2}}=\frac{(c-2)^{2}}{2(6c^{3}+15c^{2}) }$

Now let us divide the modified expressions:

$\frac{(c-2)(c+2)}{c(6c^{3}+15c^{2})}$ ÷ $\frac{(c-2)^2}{2(6c^{3}+15c^{2}) }$

we get:

$\frac{2(c+2)}{c(c-2)}$

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3 years ago

Graph the image of the figure using the transformation given. (across y=-x)

lana [24]

Answer:

The answer is B because if you take the line of y=-x (which you can look up on desmos if you don't know what y=-x looks like) and reflect over that line you can see that when the dot reflects over the line y=-x it goes to points (0,2)

Step-by-step explanation:

8 0

2 years ago

Factor this trinomial completely.

zmey [24]

First you want to write 7x as a sum or difference: 15x-8x
Now, the expression would look like this: 10x^2+15x-8x-12
Next, factor out the 5x and -4 from the expression: 5x(2x+3)-4(2x+3)
Now, factor out the 2x+3 from the expression and you have your answer:
(2x+3)(5x-4)

4 0

3 years ago

Solve the system by substitution. -8x - y = 30 -2y = x

masya89 [10]

Answer:

Solution: (-4, 2), x= -4 and y =2

Step-by-step explanation:

-8x - y = 30

-2y = x

Substitute for x

-8*(-2y) - y = 30

16y - y = 30

15y = 30

y = 30/15 = 2

Then x = -2y = -2*(2) = -4

Solution: (-4, 2), x= -4 and y =2

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2 years ago

Find the dimensions of a closed right circular cylindrical can of smallest surface area whose volume is 128pi cm^3

Ratling [72]

The surface area of a cylindrical can is equal to the sum of the area of two circles and the body of the cylinder: 2πr2 + 2πrh. volume is equal to πr2h.

V = πr2h = 128 pi
r2h = 128
h = 128/r2

A = 2πr2 + 2πrh
A = 2πr2 + 2πr*(128/r2)
A = 2πr2 + 256 π / r

the optimum dimensions is determined by taking the first derivative and equating to zero.

dA = 4 πr - 256 π /r2 = 0
r = 4 cm
h = 8 cm

4 0

2 years ago