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Valentin [98]
3 years ago
12

Refer to image given and please answer!!!!!

Mathematics
1 answer:
PtichkaEL [24]3 years ago
7 0

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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