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

Refer to image given and please answer!!!!!-example-1
User Ubermensch
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1 Answer

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Explanation:

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


(dy)/(dx) = (v(du)/(dx) - u(dv)/(dx))/(v^2)\:\:\:\:\:\:\:\:\:(1)

We can see that


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


(du)/(dx) = (8x)/(4x^2 + 1)


v(x) = 2x - 3


(dv)/(dx) = 2

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


(dy)/(dx) = ((8x(2x - 3))/((4x^2 + 1)) - 2\ln (4x^2 + 1))/((2x - 3)^2)


\:\:\:\:\:\:\:= (8x)/((4x^2 + 1)(2x - 3)) - (2\ln (4x^2 + 1))/((2x - 3)^2)

User Kamran Maximoff
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