Find the second derivative of the function defined implicitly by the equation.

Question

Find the second derivative  of the function defined implicitly by the equation.

Quizplus · Accepted Answer

To find the second derivative of an implicitly defined function, we need to differentiate the first derivative with respect to the independent variable and then substitute back the expressions of the dependent variables in terms of the independent variable. Here, we have:

First derivative: 11eaa8b1_dbae_9181_b1b6_a9b25d2fbdba_TB6026_11

Differentiating both sides with respect to x, we get:

11y' + 22xy'' = 0

Simplifying and solving for y'', we get:

y'' = -11/22 * y'/x

Now we substitute back y' and y in terms of x to get:

y' = -x/(2y)

y = (x^2)/4 + 1

Substituting back, we get:

y'' = -11x/(44y) = -11x/(44(x^2)/4 + 4) = -11x/(11x^2 + 44)

Simplifying, we get:

y'' = -1/(x^2 + 4)

Therefore, the answer is D) 11eaa8b1_dbaf_06b5_b1b6_478f4493feb2_TB6026_11.

Find the Second Derivative of the Function Defined Implicitly