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Solve the given problems by finding the appropriate derivatives.The potential $V$ (in $V$ ) of a certain electric charge is given by $V=6 /(2 t+1),$ where $t$ is the time (in s). Find $d^{2} V / d t^{2}.$

Calculus 1 / AB

Chapter 23

The Derivative

Section 9

Higher Derivatives

Derivatives

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In this problem, we have been asked to find B to b b T two. Where the function V is given as six divided by two T plus one. That means we need to find the second derivative of V. So note that this function can be rewritten as six times to t plus one to the power minus one. Now let us find the first derivative. So that will be six times the derivative of two plus one to the power minus one. Using the power rule this will be minus one times two T plus one to the power minus one minus one, which is minus two. And using the chain rule, we have to multiply this with the derivative of two, T plus one and that is equal to two. So what we end up with is minus 12 times to t plus one. Already power minus two. Next, let us determine the second derivative. That will be the derivative of this expression. Over here. Once again, we use the power rule in the chain rule, so we have minus 12 times minus two times two T plus one to the power minus two minus one, which is minus three times the derivative of two plus one, which is equal to two. So this will become equal to 48 times two T plus one to the power minus three. And this can also be written as 48 divided by two T plus one old Q. Hence the required second derivative. That is the value of V two. V. DT two is equal to 48, divided by two p plus one old Q.

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