Mathematics: Refer to image given and please answer

Refer to image given and please answer - id14088283, schnefai000

alyssa32900

26.09.2021

Step-by-step explanation:

According to the quotient rule of differentiation, if y(x) = u(x)/v(x), then its derivative is given by

$\dfrac{dy}{dx} = \dfrac{v\dfrac{du}{dx} - u\dfrac{dv}{dx}}{v^2}\:\:\:\:\:\:\:\:\:(1)$

We can see that

$u(x) = \ln (4x^2 + 1)$

$\dfrac{du}{dx} = \dfrac{8x}{4x^2 + 1}$

v(x) = 2x - 3

$\dfrac{dv}{dx} = 2$

Plugging the above expressions into Eqn(1), we find that the derivative is

$\dfrac{dy}{dx} = \dfrac{\dfrac{8x(2x - 3)}{(4x^2 + 1)} - 2\ln (4x^2 + 1)}{(2x - 3)^2}$

$\:\:\:\:\:\:\:= \dfrac{8x}{(4x^2 + 1)(2x - 3)} - \dfrac{2\ln (4x^2 + 1)}{(2x - 3)^2}$

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StupidFatChipmunk

21.08.2020

200 ft²

Step-by-step explanation:

The area of a rectangle is length times width

So, simply do 25 * 8 = 200

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