Witch of Agnesi Let y(x²+4)=8 (see figure).

Question

a. Use implicit differentiation to find dy/dx.

Accepted Answer

Hello. In this video, we are going to be calculating the derivative of the given function. The function given to us is Y multiplied by the quantity X2 + 16 equal to 64. And we want to determine the derivative DYDX. In order to find this derivative, we are going to take the derivative of the entire equation, but take the derivative with respect to X. So let's go ahead and take the derivative of the left hand side of the equation. Notice that we have a function of Y multiplied with a function of X. In order to take the derivative of the left hand side, we will need to use the product rule. By using the product rule, the derivative will be Y multiplied by the derivative X2 + 16. That will be 2 X by the power rule, and the derivative of 16 will be 0. Then we will add X2 + 16 and multiply this by the derivative of Y. Now, the derivative of Y is going to be won by the power rule. But since we are taking the derivative of Y with respect to X, that will generate a DYDX term through implicit differentiation. One, multiplied by DYDX is just going to give us DYDX. And that is going to be the derivative of the left hand side of the equation. Now, on the right-hand side, we have the constant value 64. The derivative of a constant is 0, so the derivative of the right-hand side of the equation will be 0. Now let's go ahead and solve for DYDX. We will start by multiplying Y with 2 X. That is going to give us 2 XY plus the quantity X2 + 16 multiplied by DYDX. We will subtract 2 xy to both sides of the equation. That will give us the quantity X2 + 16 multiplied by DYDX equal to -2 XY. And finally, we will divide both sides of the equation by X2 + 16. That will give us the derivative DYDX equal to -2 XY divided by X2 + 16. And this is going to be the derivative DYDX of the given equation. And with that being said, the overall solution is going to be a So, I hope this video helps you in understanding on how to approach this problem, and I will go ahead and see you all in the next video.

Witch of Agnesi Let y(x²+4)=8 (see figure). <IMAGE>
a. Use implicit differentiation to find dy/dx.

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Witch of Agnesi Let y(x²+4)=8 (see figure). <IMAGE>a. Use implicit differentiation to find dy/dx.

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Witch of Agnesi Let y(x²+4)=8 (see figure). <IMAGE>
a. Use implicit differentiation to find dy/dx.