5–8. Calculate dy/dx using implicit differentiation.

Question

x = y²

Accepted Answer

Welcome back, everyone. In this problem, we want to use implicit differentiation to calculate the derivative of Y with respect to X for the equation X2 + Y2 equals 25. A says its negative Y divided by X, B X divided by Y, C X Y, and D 2 X plus 2 Y. Now to use implicit differentiation to find the derivative of y with respect to X, it means we're going to differentiate both sides of the equation with respect to X. In other words, we need to find out the derivative with respect to X of X2 + Y2. And the derivative with respect to X of 25. Now if we differentiate both of these terms, the derivative with respect to X of X squared is 2 X. And the derivative of Y2 with respect to X. No, by implicit differentiation we can treat Y2 as a variable that can be differentiated. So we're gonna bring down the power to Y and then multiply it by D Y D X. OK, the derivative of Y with respect to X. And now on our right hand side the derivative with respect to X of the constant 25 is 0. No, we can solve for the derivative of Y with respect to X, OK? Because that's what we want. If we add, sorry, if we subtract 2 X from both sides. Then we're gonna get 2 DUIDX. To be equal to -2 x and thus the derivative of y with respect to X is going to be equal to -2 x divided by 2y which will be equal to negative X divided by Y. Thus, the derivative of Y with respect to X is negative X divided by Y. B is the correct answer. Thanks a lot for watching everyone. I hope this video helped.

5–8. Calculate dy/dx using implicit differentiation.x = y²

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5–8. Calculate dy/dx using implicit differentiation.
x = y²